Search for literature on Quantum Gravity

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  • #1
ChrisVer
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Hi all,
I am looking for a pedagogical (or maybe also historical) paper that describes the attempts of quantizing gravity and the problems that appear along the lines.
It is quite interesting to hear from public talks that "when we try to canonically quantize gravity as we did EM we get problems with divergences that don't disappear/defining time/observables" and so on. But, I would like to educate myself by seeing the problems appearing with some actual (basic) calculations. I would like to see somewhere explained how things break down by applying something that is quite known. There are many such papers for example describing the procedure we follow with the EM field. So I assume that having such a discussion paper is also a "must" for someone who is interested in going through a Quantum Gravity course/research.

E.g. how we classically define the classical (to-be-quantized) "gravitational field"?
Is it the metric?
Also it would be interesting to see how the spin-2 gravitons emerged in that approach ?
Do they appear in the same way as for example photons do when we try tried to impose gauge invariance of the EM U(1) theory?
What is the gauge invariance in the case of a metric?

If the paper gives some insight on the solutions coming from either String Theory or LQG, it would be nice but not necessary.
 

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I'm a fan of Bryce DeWitt's work, so of course I'd tell you to start with: https://journals.aps.org/pr/abstract/10.1103/PhysRev.160.1113

But, to also look at the book: Quantum Theory Of Gravity Essays in honor of the 60th birthday of Bryce DeWitt. In this book, they're not the most *formal* papers, but it is a collection of great essays from great physicists on how they approach quantum gravity.

Now, with all that being said, and I do suggest HIGHLY checking out the book if you're interested in quantum gravity, I think this is more along the lines of what you're looking for:
https://arxiv.org/abs/0907.4238

Hope this helps, and good luck! Quantum gravity is something I want to pursue, but man, it is a tough beast.
 
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  • #4
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A book that reviews all major approaches to quantum gravity:
C.Kiefer, Quantum Gravity
 
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ohwilleke
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The last three lectures in the general relativity notes.
http://home.uchicago.edu/~geroch/Course Notes
I pulled them and separated out the relevant eight pages from the whole in a pdf. The concluding few paragraphs are worth a quotation here:

We summarize by stating the formalism of this "theory". The Hilbert space is the space of all complex-valued functions Psi(h(ab)) on the space of positive-definite metrics on S, such that is invariant under the action (on h(ab)) of dieomorphisms on S, and such that
Screen Shot 2020-08-24 at 2.37.02 PM.png


We put theory in quotation marks because we have here merely an equation and a few words. What does it all mean? What is the measurement situation? What would it be like to live in such a quantum space-time? What is the correspondence limit? To what extent have the principles of quantum theory been incorporated? To what extent is this theory a "fuzzing out" of general relativity? What alternative formulations are available, and how do they compare with this one?

We are today a good way from satisfactory answers to questions of this sort.
 

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For the historical side of the OPs question this is a decent technical review of the early history of QG.

Toward a quantum theory of gravity: Syracuse 1949-1962
Donald Salisbury
Peter Bergmann and his students embarked in 1949 on a mainly canonical quantization program whose aim was to take into account the underlying four-dimensional diffeomorphism symmetry in the transition from a Lagrangian to a Hamiltonian formulation of Einstein's theory. They argued that even though one seemed to destroy the full covariance through the focus on a temporal foliation of spacetime, this loss was illusory. Early on they convinced themselves that only the construction of classical invariants could adequately reflect the fully relativistic absence of physical meaning of spacetime coordinates. Efforts were made by Bergmann students Newman and Janis to construct these classical invariants. Then in the late 1950's Bergmann and Komar proposed a comprehensive program in which classical invariants could be constructed using the spacetime geometry itself to fix intrinsic spacetime landmarks. At roughly the same time Dirac formulated a new criterion for identifying initial phase space variables, one of whose consequences was that Bergmann himself abandoned the gravitational lapse and shift as canonical variables. Furthermore, Bergmann in 1962 interpreted the Dirac formalism as altering the very nature of diffeomorphism symmetry. One class of infinitesimal diffeomorphism was to be understood as depending on the perpendicular to the given temporal foliation. Thus even within the Bergmann school program the preservation of the full four-dimensional symmetry in the Hamiltonian program became problematic. Indeed, the ADM and associated Wheeler-DeWitt program that gained and has retained prominence since this time abandoned the full symmetry. There do remain dissenters - raising the question whether the field of quantum gravity has witnessed a Renaissance in the ensuing decades - or might the full four-dimensional symmetry yet be reborn?
Comments:34 pages, to appear in Einstein Studies volume entitled The Renaissance of General Relativity edited by Alexander Blum, Roberto Lalli, and Jürgen Renn
Subjects:History and Philosophy of Physics (physics.hist-ph); General Relativity and Quantum Cosmology (gr-qc)
Cite as:arXiv:1909.05412 [physics.hist-ph]
(or arXiv:1909.05412v1 [physics.hist-ph] for this version)
 
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robphy
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https://iopscience.iop.org/article/10.1088/0034-4885/37/10/001/meta

Quantum theory of gravitation
A Ashtekar and R Geroch
Reports on Progress in Physics, Volume 37, Number 10 (1974)

Attempts to obtain a quantum theory of gravitation are reviewed. The essential ideas of those programmes on which extensive work has been done are discussed. Successes and difficulties of each of these programmes are described. The attempts are divided into two broad classes: those based on the techniques of canonical quantization and those based on the techniques of quantum field theory. The authors approach is rather geometrical, an approach which facilitates the comparison of various programmes.
 
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  • #12
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The more I read papers and books by Geroch, the more impressed I am. What a great physicist!
I enjoyed every class I attended.
I’ve been inspired to develop my geometrical thinking.

recently, he posted a lot of scanned notes...
https://home.uchicago.edu/~geroch/
(The parent folder of the relativity notes posted earlier.)
 
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This is quite good for genealogy

https://www.genealogy.math.ndsu.nodak.edu/
Yes, it’s been around for a while... and is more extensive. However, it’s still missing a bunch of Bergmann’s students. As a Syracuse grad, I should contribute the missing entries.
 

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