Getting Started With Bryce Dewitts Lectures On Gravitation Bryce Dewitt
The DeWitt lectures on gravitation are a set of advanced physics notes and recordings that cover the canonical formalism of general relativity, quantum field theory in curved spacetime, and the early development of what became known as Wheeler-DeWitt equation stuff. They are not beginner material. If you are coming in cold from an undergraduate GR course, you will get lost fast. I learned that the hard way. Bryce DeWitt was a prominent theoretical physicist at Cornell and later at the University of Texas. His lectures, especially the ones from the 1960s and 70s, became foundational texts for quantum gravity research. The most cited version is his contribution to the 1964 CERN summer school lectures, later expanded and republished. The core material deals with the Hamiltonian formulation of general relativity, constraint analysis, path integrals over geometries, and the early attempts at quantizing gravity using canonical methods. The phrase Bryce Dewitts Lectures On Gravitation Bryce Dewitt keeps coming up in search results because the material has been republished, mirrored, and discussed across numerous physics forums and academic sites over the decades. The original source is generally traced back to his CERN 1964 lectures and his Les Houches 1967 contributions. Some versions are available through academic repositories. Others exist as scanned PDFs on physics mailing list archives.
How I actually used them
I ran into these lectures while trying to understand the ADM formalism beyond what the standard textbooks cover. MTW has the basics, but DeWitt goes deeper into the path integral approach and the treatment of constraints. I needed this for work on numerical relativity initial data construction, specifically the way constraints propagate or fail to propagate in certain gauge choices. The practical approach that worked for me was not to read cover to cover. I picked the sections on the Hamiltonian constraint and the momentum constraint, worked through the derivations by hand, and then checked them against the original ADM paper from 1962. DeWitt notates things slightly differently than ADM, and that difference matters when you are actually implementing the equations in code. He uses a different sign convention for the Ricci scalar in the action, which flips the sign of the Hamiltonian constraint relative to what you see in some other references. If you are coding this stuff up, getting that sign wrong means your constraint violation grows instead of shrinking, and you will not know why until you have spent several hours debugging something that was a convention issue all along.
Where to find them
The most reliable source I have found is through the CERN Document Server, where DeWitt's 1964 lectures are archived under the title "The Quantum Theory of Gravity." There are also copies hosted on various university physics department servers and on arXiv-related mirrors. Search for DeWitt 1964 CERN lectures gravitation. Some versions are in French translation from the original lectures. The English versions are the standard reference. There are also compilations that include DeWitt's work alongside other lectures in the same volumes, particularly the 1967 Les Houches proceedings. These are sometimes harder to track down since they were published in older book formats before open access became common. If you have university library access, look for the Durbin volume from the 1964 CERN school or the 1967 Les Houches Proceedings, Session VII, which is titled "Gravitation, Groups, and Particles."
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Common pitfalls and what the lectures do not cover
The biggest limitation of these lectures is that they are dated. DeWitt wrote them in the 1960s. The mathematical physics landscape has moved on significantly. Modern treatments of the same material, particularly in Loop Quantum Gravity and modern canonical quantum gravity, build on and sometimes correct DeWitt's approach. You should not treat these lectures as the final word on any topic they touch. Another issue is that DeWitt assumes a very high level of mathematical maturity. He does not spell out every step. If you are not comfortable with functional analysis, infinite-dimensional manifolds, and the theory of distributions, you will struggle. I have seen graduate students spend weeks trying to follow derivations that DeWitt sketches in a page or two. The workaround is to keep a modern text on hand. I found that Hartle's "Gravitation" notes and more recently Rovelli's "Quantum Gravity" help fill in some of the gaps, though they cover different aspects. The lectures also do not cover perturbative quantum gravity beyond the basic framework. If you are looking for material on graviton scattering amplitudes or modern effective field theory approaches to gravity, these lectures are not the place. For that, look at works by 't Hooft and Veltman, or the more recent reviews by Burgess and others on the effective field theory treatment of gravity.
A specific edge case I ran into
While working through the constraint algebra section, I noticed that DeWitt's treatment of the smeared constraints uses a notation that conflates the smearing functions with the lapse and shift in a way that is easy to misinterpret if you are not careful. The Poisson bracket algebra of constraints closes only when you use the correct smearing. I was working on a project involving the evolution of constraint violations in a numerical scheme, and I initially got the bracket computation wrong because I did not properly track which terms were being smeared and which were not. The fix was to go back to the original ADM paper and carefully compare their notation with DeWitt's. The physics is the same, but the bookkeeping is different. Spending an afternoon on that comparison saved me from building a numerical code on top of an incorrect constraint algebra.
Bottom line
The DeWitt lectures remain a valuable resource for anyone working in canonical quantum gravity or needing a deep understanding of the Hamiltonian structure of general relativity. They are not easy. They are not complete by modern standards. But they are still the source that many people in the field go back to when they need the original derivation or a different perspective on the constraint structure. If you can handle the mathematical level and take the time to cross-reference with more modern sources, they will serve you well. If you are looking for a gentle introduction, start elsewhere and come back to these once you know what you are looking for.
