Quantum Gravity

In General > s.a. 2D quantum gravity; 3D quantum gravity; canonical, covariant, histories, and other approaches.
* Idea: A theory describing the structure of spacetime down to subplanckian scales, and for an arbitrary number of occupied states; Often considered as a theory in which the spacetime metric is quantized (beyond quantum field theory in curved spacetime or semiclassical gravity – includes back-reaction), as well as possibly other geometrical structures – it describes gravitation as well as quantum geometry.
* History: Serious work on quantum gravity began in the early 1950's; Until the 1970's only gravity included.
* Goal: Want to get complete, consistent theory with well-defined general relativity limit.
* Difficulties: (1) g_ab is both gravitational field and metric, there is no background metric, so how to write canonical commutation relations?; (2) Perturbative non-renormalizability, which could be similar to the UV catastrophe before quantum mechanics (> see covariant quantum gravity); (3) Unbounded action; (4) Conceptual difficulty, What is time, What are the observables? (5) The need to incorporate the full diffeomorphism group as symmetry group.
* Issues: How much to retain of the classical general relativity technical and conceptual structure? How much of quantum theory? What matter to include? Which predictions do we expect to get? What is the vacuum? Is the theory unitary? CPT invariant? Is gravity geometrical at the quantum level? (There are arguments to the contrary, based on gravity-induced interference, > see wave phenomena); Must quantum gravity be background-independent? (Related to relational vs absolute spacetime debate).
* Interpretation: Within "conventional" interpretations, the many-worlds is possible; The Copenhagen and the statistical ones require some "mental acrobacies"; & Banks; Susskind; Unruh & Wald.

On Whether to Quantize > s.a. general relativity; semiclassical general relativity [problems].
* Pro: (0) Similarity with other theories; (1) Structure of Einstein's equation, and inconsistency of a quantum field theory on a curved background, or semiclassical general relativity, with back-reaction; (2) Remove the singularities predicted by the classical theory (by, say, interference between amplitudes for various geometries, smearing of light-cones, cancellations in supergravity); (3) Understand black hole thermodynamics; (4) Help us understand why the renormalization methods work and get a coherent picture of quantum field theories of all interactions (may help in unification).
* Alternatives: Some people (& Narlikar, Padmanabhan) have proposed to quantize only the conformal factor; Would be natural in the null-surface approach to general relativity, but not convincing.
@ References: Page & Geilker PRL(81); von Borzeszkowski FP(90); Drechsler FP(93); Anandan GRG(94); Huggett & Callender PhSc(01)sep; Mohrhoff MPLA(02)qp, de Souza gq/02, Cooperstock IJMPD(05) [no]; Kent gq/05 [causality test]; Wüthrich PhSc(05)dec [effective gravity as alternative]; Albers et al a0802 [justification does not follow from logical arguments alone]; Carlip a0803-in [not conclusive].

Consequences and Techniques > s.a. quantum fields in curved spacetime; quantum cosmology; quantum spacetime.
* Particle physics: Consequences are expected to manifest themselves mostly at Planck scales; Baryon number violation in black hole formation and evaporation; CP and CPT violation, distinguished from GUT effects; Suppression of ultra-high energy scattering amplitudes.
@ Information loss: Schiffer GRG(93); Srednicki NPB(93); Itzhaki CQG(95)ht.
@ Statistical methods: Damgaard et al ed-90; Botelho PRD(95) [random surfaces]; Ambjørn et al 97; > s.a. geometrodynamics.
@ Related topics: Husain & Jaimungal MPLA(99), gq/99-in [phase transitions]; Raptis gq/06 [abstract differential geometry].
> Computational: see computational physics, Stephen Braham's 1995 page.
> Phenomenology: see general, in cosmology, matter, photons; collapse; inflation; semiclassical quantum gravity [including stability].
> Related issues: see anomaly; Correspondence Principle; Covariance; CP violation; CPT; differential geometry; effective action; renormalization; symmetry breaking; time; vacuum.

References > s.a. anthropic; history of physics.
@ I/II: Ashtekar Rech(84); Gibbons NS(85); Sánchez 87; Isham in(89); PW(90)mar; Renteln AS(91); Au gq/95; Hawking & Penrose SA(96)jul; Norbury EJP(98)phy; Smolin pw(99)dec; Amelino-Camelia Nat(00)gq; Smolin 00 [r AS(02)jan]; Chalmers pw(03)nov + issue; Hammond 08.
@ Reviews: Isham in(75), in(81), in(86), pr(91), CQG(96); Ashtekar ht/94-in; Shiekh gq/96-in; Rovelli gq/98-in; Wallace gq/00; Horowitz gq/00-in; Kiefer LNP(03); Smolin ht/03; Isham qp/04-in [categorical]; Álvarez gq/04-ln; Ashtekar NJP(05)gq/04; Kiefer AdP(06)gq/05; Rovelli gq/06-in; Markopoulou gq/07-in [background-independent]; Booss-Bavnbek et al Sigma(07)-a0708; DeWitt & Esposito IJGMP(08)-a0711-ln.
@ Texts: Narlikar & Padmanabhan 87; von Borzeszkowski & Treder 88; Prugovecki 92, 95; Pavsic 01; Rovelli 04; Kiefer 07.
@ General: Rosenfeld AdP(30); Misner RMP(57); Arnowitt & Deser PR(59); Bergmann & Komar in(62); DeWitt in(62), in(63); Bergmann pr(69); Komar IJTP(69); DeWitt GRG(70); Bergmann GRG(71); Ashtekar & Geroch RPP(74); DeWitt in(79); Ashtekar CS(80); Padmanabhan IJMPA(89); Prugovecki FP(92); Penrose in(88); Álvarez RMP(89), in(92); Hu gq/96-in.
@ Conceptual: Isham gq/93-in [prima facie questions], gq/95-in [structural issues]; von Borzeszkowski & Treder GRG(93) [difficulties from equivalence principle]; Padmanabhan in(99)ht/98; Butterfield & Isham gq/99-in; Rovelli JMP(00)gq/99; Aerts IJTP(96); 't Hooft SHPMP(01); Cao SHPMP(01) [ontological synthesis]; Carlip RPP(01)gq; Padmanabhan CQG(02)gq/01-in; Rovelli IJMPD(03)ht [and strings, dialog]; Smolin ht/05 [background independence]; Stachel gq/05-in, gq/06; Rickles SHPMP(05) [interpretation]; Rosinger qp/05 [questions]; Sudarsky IJMPD(08)-a0712-in [unspeakables]; Rosen FP(08); > s.a. logic.
@ And hep/strings: Maldacena IJMPA(00)hp-in; Álvarez gq/03-in; Bjerrum-Bohr ht/04-PhD.
@ And quantum info/computation: Zizzi GRG(01)gq/00-in; Lloyd qp/05/Sci; Girelli & Livine CQG(05)gq [with spin networks]; Terno gq/05-in [lqg and black holes]; > s.a. black holes [as computers], black hole thermodynamics, discrete spacetime, quantum information.
@ Collections: Isham et al 75; Isham et al 81; Duff & Isham 82; Christensen 84; Markov et al 85, 88; Gibbons & Hawking 93 [euclidean]; Rickles et al ed-06 [structural, r CQG(07)]; Fauser et al 07 [techniques].

Online Resources
> Websites: see Qgravity.org site; Quantum Spacetime and Fields site; Cambridge University quantum gravity site.
> Pages and articles: see John Baez's seminar; Seth Major's page; John Barrett's page; Wikipedia page; Answers.com page; Ken Koehler's site; Stephen Wolfram's page.

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 11 jul 2008