| communications in mathematical physics: The Physics and Mathematics of Electromagnetic Wave Propagation in Cellular Wireless Communication Tapan K. Sarkar, Magdalena Salazar Palma, Mohammad Najib Abdallah, 2018-07-18 An important resource that examines the physical aspects of wireless communications based on mathematical and physical evidence The Physics and Mathematics of Electromagnetic Wave Propagation in Cellular Wireless Communicationdescribes the electromagnetic principles for designing a cellular wireless system and includes the subtle electromagnetic principles that are often overlooked in designing such a system. This important text explores both the physics and mathematical concepts used in deploying antennas for transmission and reception of electromagnetic signals and examines how to select the proper methodology from a wide range of scenarios. In this much-needed guide, the authors—noted experts in the field—explore the principle of electromagnetics as developed through the Maxwellian principles and describe the properties of an antenna in the frequency domain. The text also includes a review of the characterization of propagation path loss in a cellular wireless environment and examines ultrawideband antennas and the mechanisms of broadband transmission of both power and information. This important resource: Includes a discussion of the shortcomings of a MIMO system from both theoretical and practical aspects Demonstrates how to deploy base station antennas with better efficiency Validates the principle and the theoretical analysis of electromagnetic propagation in cellular wireless communication Contains results of experiments that are solidly grounded in mathematics and physics Written for engineers, researchers, and educators who are or plan to work in the field, The Physics and Mathematics of Electromagnetic Wave Propagation in Cellular Wireless Communicationoffers an essential resource for understanding the principles underpinning wireless communications. |
| communications in mathematical physics: The Mathematical Theory of Communication Claude E Shannon, Warren Weaver, 1998-09-01 Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic. |
| communications in mathematical physics: Number Theory and Physics Jean-Marc Luck, Pierre Moussa, Michel Waldschmidt, 2012-12-06 7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with small denominators, as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string theory of fundamental interactions, completely integrable models, and conformally invariant two-dimensional field theories, seems to involve modular forms and p adic numbers in a remarkable way. |
| communications in mathematical physics: The Boltzmann Equation E.G.D. Cohen, W. Thirring, 2012-12-06 In,1872, Boltzmann published a paper which for the first time provided a precise mathematical basis for a discussion of the approach to equilibrium. The paper dealt with the approach to equilibrium of a dilute gas and was based on an equation - the Boltzmann equation, as we call it now - for the velocity distribution function of such ~ gas. The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the excitation gas in a superfluid. Therefore it was felt by many of us that the Boltzmann equation was of sufficient interest, even today, to warrant a meeting, in which a review of its present status would be undertaken. Since Boltzmann had spent a good part of his life in Vienna, this city seemed to be a natural setting for such a meeting. The first day was devoted to historical lectures, since it was generally felt that apart from their general interest, they would furnish a good introduction to the subsequent scientific sessions. We are very much indebted to Dr. D. |
| communications in mathematical physics: Algorithms for Computer Algebra Keith O. Geddes, Stephen R. Czapor, George Labahn, 2007-06-30 Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields. |
| communications in mathematical physics: Mathematics for Future Computing and Communications Liao Heng, Bill McColl, 2021-12-16 A panorama of new ideas in mathematics that are driving innovation in computing and communications. |
| communications in mathematical physics: Nonlinear Optics D.L. Mills, 2012-12-06 Intended for readers with a background in classical electromagnetic theory, this book develops the basic principles that underlie nonlinear optical phenomena in matter. It begins with a discussion of linear wave propagation in dispersive media, moves into weak nonlinearities which can be discussed in a pertuberative manner, then it examines strong nonlinear effects (solitons, chaos). The emphasis is on the macroscopic description on nonlinear phenomena, within a semiclassical framework. Two new chapters cover surface optics and magneto-optic phenomena. The book is aimed at the student or researcher who is not a specialist in optics but needs an introduction to the principal concepts. |
| communications in mathematical physics: The Geometry and Physics of Knots Michael Francis Atiyah, 1990-08-23 These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. |
| communications in mathematical physics: Decorated Teichmüller Theory R. C. Penner, 2012 There is an essentially ``tinker-toy'' model of a trivial bundle over the classical Teichmuller space of a punctured surface, called the decorated Teichmuller space, where the fiber over a point is the space of all tuples of horocycles, one about each puncture. This model leads to an extension of the classical mapping class groups called the Ptolemy groupoids and to certain matrix models solving related enumerative problems, each of which has proved useful both in mathematics and in theoretical physics. These spaces enjoy several related parametrizations leading to a rich and intricate algebro-geometric structure tied to the already elaborate combinatorial structure of the tinker-toy model. Indeed, the natural coordinates give the prototypical examples not only of cluster algebras but also of tropicalization. This interplay of combinatorics and coordinates admits further manifestations, for example, in a Lie theory for homeomorphisms of the circle, in the geometry underlying the Gauss product, in profinite and pronilpotent geometry, in the combinatorics underlying conformal and topological quantum field theories, and in the geometry and combinatorics of macromolecules. This volume gives the story a wider context of these decorated Teichmuller spaces as developed by the author over the last two decades in a series of papers, some of them in collaboration. Sometimes correcting errors or typos, sometimes simplifying proofs, and sometimes articulating more general formulations than the original research papers, this volume is self contained and requires little formal background. Based on a master's course at Aarhus University, it gives the first treatment of these works in monographic form. |
| communications in mathematical physics: XVIIth International Congress on Mathematical Physics Arne Jensen, 2014 This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals. |
| communications in mathematical physics: Software Pioneers Manfred Broy, Ernst Denert, 2012-12-06 A lucid statement of the philosophy of modular programming can be found in a 1970 textbook on the design of system programs by Gouthier and Pont [1, l Cfl0. 23], which we quote below: A well-defined segmentation of the project effort ensures system modularity. Each task fonos a separate, distinct program module. At implementation time each module and its inputs and outputs are well-defined, there is no confusion in the intended interface with other system modules. At checkout time the in tegrity of the module is tested independently; there are few sche duling problems in synchronizing the completion of several tasks before checkout can begin. Finally, the system is maintained in modular fashion; system errors and deficiencies can be traced to specific system modules, thus limiting the scope of detailed error searching. Usually nothing is said about the criteria to be used in dividing the system into modules. This paper will discuss that issue and, by means of examples, suggest some criteria which can be used in decomposing a system into modules. A Brief Status Report The major advancement in the area of modular programming has been the development of coding techniques and assemblers which (1) allow one modu1e to be written with little knowledge of the code in another module, and (2) alJow modules to be reas sembled and replaced without reassembly of the whole system. |
| communications in mathematical physics: Differential Forms in Mathematical Physics , 2009-06-17 Differential Forms in Mathematical Physics |
| communications in mathematical physics: The Mathematical Theory of Communication Claude Elwood Shannon, Warren Weaver, 1962 |
| communications in mathematical physics: Quantum Fields in Curved Space N. D. Birrell, P. C. W. Davies, 1984-02-23 This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level. |
| communications in mathematical physics: Variational Principles in Mathematical Physics, Geometry, and Economics Alexandru Kristály, V. Rădulescu, Vicenţiu D. Rădulescu, Csaba Varga, 2010-08-19 A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations. |
| communications in mathematical physics: Exactly Solved Models in Statistical Mechanics Rodney J. Baxter, 2016-06-12 Exactly Solved Models in Statistical Mechanics |
| communications in mathematical physics: Mathematical Optics Vasudevan Lakshminarayanan, María L. Calvo, Tatiana Alieva, 2012-12-14 Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at www.crcpress.com. |
| communications in mathematical physics: Mathematics for Physics Michael M. Woolfson, Malcolm S. Woolfson, 2007 Mathematics for Physics features both print and online support, with many in-text exercises and end-of-chapter problems, and web-based computer programs, to both stimulate learning and build understanding. |
| communications in mathematical physics: Gravity and Strings Tomás Ortín, 2015-03-26 Self-contained and comprehensive, this definitive new edition provides a complete overview of the intersection of gravity, supergravity, and superstrings. |
| communications in mathematical physics: Mathematics for Physics Michael Stone, Paul Goldbart, 2009-07-09 An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030. |
| communications in mathematical physics: Positive Linear Maps of Operator Algebras Erling Størmer, 2012-12-13 This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout. |
| communications in mathematical physics: Philosophy of Physics Jeremy Butterfield, John Earman, 2007 The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman's chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, 't Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers |
| communications in mathematical physics: Tau Functions and their Applications John Harnad, Ferenc Balogh, 2021-02-04 A thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics. |
| communications in mathematical physics: The Philosophy and Physics of Noether's Theorems James Read, Nicholas J. Teh, 2022-08-31 In 1918, Emmy Noether, in her paper Invariante Variationsprobleme, proved two theorems (and their converses) on variational problems that went on to revolutionise theoretical physics. 100 years later, the mathematics of Noether's theorems continues to be generalised, and the physical applications of her results continue to diversify. This centenary volume brings together world-leading historians, philosophers, physicists, and mathematicians in order to clarify the historical context of this work, its foundational and philosophical consequences, and its myriad physical applications. Suitable for advanced undergraduate and graduate students and professional researchers, this is a go-to resource for those wishing to understand Noether's work on variational problems and the profound applications which it finds in contemporary physics. |
| communications in mathematical physics: Introduction to Classical Integrable Systems Olivier Babelon, Denis Bernard, Michel Talon, 2003-04-17 This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field. |
| communications in mathematical physics: The Large Scale Structure of Space-Time S. W. Hawking, G. F. R. Ellis, 1975-02-27 Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book. |
| communications in mathematical physics: The Kernel Function and Conformal Mapping Stefan Bergman, 1950-03 The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of The Kernel Function. The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable. |
| communications in mathematical physics: Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday Fritz Gesztesy, 2007 This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume. |
| communications in mathematical physics: Mathematics and Physics for Nanotechnology Paolo Di Sia, 2019-02-05 Nanobiotechnology is a new interdisciplinary science with revolutionary perspectives arising from the fact that at nanosize the behaviour and characteristics of matter change with respect to ordinary macroscopic dimensions. Nanotechnology is a new way for producing and getting materials, structures and devices with greatly improved or completely new properties and functionalities. This book provides an introductory overview of the nanobiotechnology world along with a general technical framework about mathematical modelling through which we today study the phenomena of charge transport at the nanometer level. Although it is not a purely mathematics or physics book, it introduces the basic mathematical and physical notions that are important and necessary for theory and applications in nanobiotechnology. Therefore, it can be considered an extended formulary of basic and advanced concepts. It can be the starting point for discussions and insights and can be used for further developments in mathematical–physical modelling linked to the nanobiotechnology world. The book is dedicated to all those who follow their ideas in life and pursue their choices with determination and firmness, in a free and independent way. |
| communications in mathematical physics: Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics Josi A. de Azcárraga, Josi M. Izquierdo, 1998-08-06 A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics. |
| communications in mathematical physics: Rigorous Quantum Field Theory Anne Boutet de Monvel, Detlev Buchholz, Daniel Iagolnitzer, Ugo Moschella, 2006-12-15 Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous contributions; this book arose from an international symposium held in honour of Bros on the occasion of his 70th birthday. Key topics in this volume include: Analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime. |
| communications in mathematical physics: Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry Roger Penrose, Wolfgang Rindler, 1984 In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields. |
| communications in mathematical physics: Mathematical Physics with Differential Equations YISONG. YANG, 2023-02-20 Traditional literature in mathematical physics is clustered around classical mechanics, especially fluids and elasticity. This book reflects the modern development of theoretical physics in the areas of field theories: classical, quantum, and gravitational, in which differential equations play essential roles and offer powerful insight. Yang here presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general relativity, superconductivity, vortices and other topological solitons, and canonical quantization of fields, for which knowledge and use of linear and nonlinear differential equations are essential for comprehension. Much emphasis is given to the mathematical and physical content offering an appreciation of the interplay of mathematics and theoretical physics from the viewpoint of differential equations. Advanced methods and techniques of modern nonlinear functional analysis are kept to a minimum and each chapter is supplemented with a collection of exercises of varied depths making it an ideal resource for students and researchers alike. |
| communications in mathematical physics: Analysis And Mathematical Physics Shaun Bullett, Tom Fearn, Frank Smith, 2016-12-22 This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics.Analysis and Mathematical Physics is the sixth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas. |
| communications in mathematical physics: Mathematics and Materials Mark J. Bowick, David Kinderlehrer, Govind Menon, Charles Radin, 2017-08-25 A co-publication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics Articles in this volume are based on lectures presented at the Park City summer school on “Mathematics and Materials” in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics. The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. NOTE: This discount does not apply to volumes in this series co-published with the Society for Industrial and Applied Mathematics (SIAM). |
| communications in mathematical physics: Geometry of String Theory Compactifications Alessandro Tomasiello, 2022-01-13 A unified perspective on new and advanced mathematical techniques used in string theory research for graduate students and researchers. |
| communications in mathematical physics: Renormalization Group Giuseppe Benfatto, Giovanni Gallavotti, 2020-11-10 Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties. |
| communications in mathematical physics: Percolation Geoffrey R. Grimmett, 2013-03-09 Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications. |
| communications in mathematical physics: Issues in Applied Mathematics: 2013 Edition , 2013-05-01 Issues in Applied Mathematics / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Mathematical Physics. The editors have built Issues in Applied Mathematics: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Physics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/. |
| communications in mathematical physics: Issues in Applied Mathematics: 2011 Edition , 2012-01-09 Issues in Applied Mathematics / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Applied Mathematics. The editors have built Issues in Applied Mathematics: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Applied Mathematics in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/. |
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Entropy Inequalities 161 exists for any orthonormal basis {ψj} and 0 ^ S ^ + oo. If S < oo for one basis {ψj}, then the nonnegative operator — ρlnρ is in the trace class and hence S is …
Quantized Fields Propagating in Plane-Wave Spacetimes
Quantized Fields in Plane-Waves 193 where ^(x, x') is a certain (Bogoliυbov invariant) solution of the homogeneous Klein-Gordon equation, which was defined in [3].
Communications in - Project Euclid
Communications in Commun. Math. Phys. 127, 529-553 (1990) Mathematical Physics ... Cambridge CB3 9EW, UK 2 Department of Physics, The Pennsylvania State University, …
Topological Gauge Theories and Group Cohomology
way to two dimensional mathematical physics [1] and are interesting as well for their purely geometrical content. One of the key ingredients in formulating three dimensional topological …
The Equations of Magnetohydrodynamics: On the Interaction …
Commun. Math. Phys. 266, 595–629 (2006) Communications in Mathematical Physics The Equations of Magnetohydrodynamics: On the Interaction Between Matter and Radiation in the …
Existence of Solitary Waves in Higher Dimensions* - Springer
Communications in Mathematical Physics O by Springer-Verlag 1977 Existence of Solitary Waves in Higher Dimensions* Walter A. Strauss Department of Mathematics, Brown University, …
Integration with Respect to the Haar Measure on Unitary
Commun. Math. Phys. 264, 773–795 (2006) Communications in Mathematical Physics Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group Benoˆıt …
Physics
in condensed matter physics. In [FSW,BV, and PI], for instance, infinite dimensional invariant tori were constructed for some approximate models of anharmonic, disordered, crystals. More …
Discrete Riemann Surfaces and the Ising Model
Finally, for applications of this theory to statistical physics, one needs to define a discrete analogue of spinor fields on Riemann surfaces. In Sect. 4 we first define the notion of a …
Qualitative Analysis for a New Integrable Two-Component
Commun. Math. Phys. 336, 581–617 (2015) Communications in Mathematical Physics Qualitative Analysis for a New Integrable Two-Component Camassa–Holm System with Peakon and …
On Witten's Proof of the Positive Energy Theorem* - Project …
The Positive Energy Theorem 227 This vector bundle—also denoted S—carries the inner products (,) and <,>. Sections of S are called Dirac spinors along M. - > The metric connection …
Special Geometry - Project Euclid
Special Geometry 165 holomorphic section Ω of Jtf ® L whose norm is the exponential of the Kahler potential on Jί. We will show that this implies the existence of special coordinates in …
Bosonization on Higher Genus Riemann Surfaces1 - Project …
3 Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA Abstract. We prove the equivalence between certain fermionic and bosonic theories in two spacetime …
Communications Mathematical Physics - University of …
Communications in Mathematical Physics @ by Springer-Verlag 1978 A Lower Bound for the Mass of a Random Gaussian Lattice* ... 1. Lieb, E., Mattis, D.: Mathematical physics in one …
Mathematical Physics
Local Fluctuation of Spectra of Anderson Models 713 Now let us describe the basic idea behind our theorem. First note that the con-dition (1.4-5) and (1.20) imply that we have Anderson …
Communications in Mathematical Physics - ISU Sites
Communications in Mathematical Physics On the mixed-unitary rank of quantum channels--Manuscript Draft--Manuscript Number: CIMP-D-20-00358 ... 4Perimeter Institute for …
Mathematical Physics - Project Euclid
"Communications in Mathematical Physics" publishes original articles in theo-retical physics and, on occasion, mathematical contributions which are of direct interest to the theoretical physicist. …
Anderson Localization for the Almost Mathieu Equation, III.
Anderson Localization for Almost Mathieu Equation. III 5 Note that 2 = f : for every s>r(!) the relation jsin2ˇ( +(j=2)!)j
Quantum Conditional Mutual Information and Approximate
Commun. Math. Phys. 340, 575–611 (2015) Communications in Mathematical Physics Quantum Conditional Mutual Information and Approximate Markov Chains Omar Fawzi1,2, Renato …
Random graph asymptotics on high-dimensional tori
Our method is crucially based on the results in [8, 9], but we also rely on mean-field results for percolation on Zd by Hara [14, 15], Hara and Slade [16], and Hara, van der Hofstad and Slade …
Determining a Random Schrödinger Operator: Both Potential …
Commun. Math. Phys. 381, 527–556 (2021) Communications in Mathematical Physics Determining a Random Schrödinger Operator: Both Potential and Source are Random Jingzhi …
MIT Open Access Articles - Massachusetts Institute of …
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, LISA Michal Horodeckit Institute for Theoretical Physics and Astrophysics, University of Gdaúsk, 80 …
Commun. Math. Phys. 99,177-195 (1985) Physics - Project Euclid
Dec 5, 1984 · 180 J. Milnor Note. In the literature, the set ρ(A) is usually called the "basin of attraction" if it is an open set, and the "stable manifold" if it is a lower dimensional smooth …
Symmetry and Related Properties via the Maximum Principle
Symmetry via the Maximum Principle 213 one obtains where L is an elliptic operator containing no zero-order term. Thus 0 g L'v + v(a ll v2 Jrb 1 ot + c) = L'v + cfv. For a sufficiently large, c'^.0. …
Index Theory of One Dimensional Quantum Walks and …
Math. Phys. 310, 419–454 (2012) Communications in Mathematical Physics Index Theory of One Dimensional Quantum Walks and Cellular Automata D. Gross1,2,V.Nesme1,3,H.Vogts1, R.F. …
Communications Mathematical Physics - Springer
8 I.M. Singer integrate over s(91) with a weight factor the Jacobian change of variables of p:s(91)~91. The determinant weight factor is interpreted as the integral of a
Efficient Quantum Algorithms for Simulating Sparse Hamiltonia
Digital Object Identifier (DOI) 10.1007/s00220-006-0150-x Commun. Math. Phys. 270, 359–371 (2007) Communications in Mathematical Physics Efficient Quantum Algorithms for Simulating …
Quantum Field Theory and the Jones Polynomial - School of …
and it has always been clear that it was connected with mathematical physics at least at the level of classical nonlinear equations. The puzzle about Donaldson theory was whether this theory …
On Quadratic First Integrals of the Geodesic Equations for …
266 M. Walker and R. Penrose: equations t° V c ta = 0 greatly facilitates the extension of a locally given spacetime to a maximal inextendible spacetime (and hence the global analysis of (M, g …
Axial Anomalies and Index Theorems on Open Spaces
Axial Anomalies and Index Theorems on Open Spaces 217 is bounded away from 0 for \x\ ^ C. Conversely, if A is Fredholm from [Hm(IRn)]M to [L2(Rn)]M then there exist such constants c …
Communications in Mathematical Physics - arXiv.org
Communications in Mathematical Physics Roman Kotecky, 1 Alan D. Sokal,2 Jan Swart3 ENTROPY-DRIVEN PHASE TRANSITION IN LOW-TEMPERATURE …
Topological gauge theories and group cohomology - Springer
Communications in Mathematical Physics 9 Springer-Verlag 1990 Topological Gauge Theories and Group Cohomology Robbert Dijkgraaf 1. and Edward Witten 2 1 Institute for Theoretical …
Communications In Mathematical Physics
622 V. Jaksic, C.-A. Fillet with Γjk = π\(ψ k,Qψj)\2g β (Ej - E k) . (1.11) Here the weight gβ is given, in terms, of the form factor α, by the following formula: where the integral is over the unit …
ANDREA AGAZZI - Duke University
Communications in Mathematical Physics (2023), “A homotopic approach to policy gradients for linear quadratic regulators with nonlinear con-trols”, with C. Chen. IEEE 61st Conference on …
Free Products of Compact Quantum Groups - Project Euclid
for some fruitful conversations and communications; S. L. Woronowicz, for commu-nicating to him a unitary matrix that is used in this paper to prove the non-existence of Woronowicz C* …
Communications Mathematical Physics
Communications in Mathematical Physics @ by Springer-Verlag 1978 A Lower Bound for the Mass of a Random Gaussian Lattice* David Brydges 1 and Paul Federbush 2 a Rockefeller …
Calculation of Norms of Bethe Wave Functions - Project Euclid
Calculation of Norms of Bethe Wave Functions 395 Here the φ κ are the variables (2.23) and the set of the λ is a solution of the system (2.18) (2.6). The derivatives can be written in the explicit …
A Conformally Invariant Gap Theorem in Yang–Mills Theory
Commun. Math. Phys. 361, 1155–1167 (2018) Communications in Mathematical Physics A Conformally Invariant Gap Theorem in Yang–Mills Theory Matthew Gursky1, Casey Lynn …
Communications in Mathematical Physics
Fax (201)348-4505 Members of the International Association of Mathematical Physics (IAMP) are entitled to receive the journal strictly for their own personal use at a special reduced rate. ...
Commun. Math. Phys. 401, 1059–1060 (2023) …
Commun. Math. Phys. 401, 1059–1060 (2023) Communications in Mathematical Physics Correction Correction to: Exponentially Small Splitting of Separatrices Associated to 3D …
Entropy Accumulation - Springer
Entropy Accumulation 869 M1 M2 ··· Mn A1 B1 A2 B2 An Bn R0 R1 R2 Rn−1 Fig. 1. Circuit diagram illustrating the decomposition of states ρAn 1B n 1 relevant for our main theorem. …
Entanglement Monogamy via Multivariate Trace Inequalities
Commun. Math. Phys. (2024) 405:29 Communications in Mathematical Physics Entanglement Monogamy via Multivariate Trace Inequalities Mario Berta1, Marco Tomamichel2,3 1 Institute …
Communications Commun. Math. Phys. 76, 289-301 (1980) …
physics where this structure seems to have been first introduced). We show on G.C.S.M. examples that the components of the metric tensor are related to the dispersion of the …
Thermodynamics of Black Holes in Anti-de Sitter Space
1 University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England 2 Department of Physics, The Pennsylvania State University, …
Geometry of Quantum States - Project Euclid
Geometry of Quantum States 57 If assumptions I, II, III hold, the analogy between the set Q and a logical system can be established as follows. We call each filter α ζ Q a proposition. The …
The Four Laws of Black Hole Mechanics - Springer
Department of Physics, Yale University, New Haven, Connecticut, USA B. Carter and S. W. Hawking Institute of Astronomy, University of Cambridge, England Received January 24, 1973 …
Physics
Jan 9, 1978 · Communications in Commun. math. Phys. 60, 153—170 ... [6, 11], there are other fields of physics where this theory is the basis for the connection between quantum mechanics …
GlobalExistenceandFinite-TimeBlow-UpforaNonlinear …
Commun. Math. Phys. 402, 3233–3252 (2023) Communications in Mathematical Physics GlobalExistenceandFinite-TimeBlow-UpforaNonlinear Nonlocal Evolution Equation Adrian …
