Approaches to Quantum Gravity  

In General, "Conventional" Approaches > s.a. [quantum gravity, phenomenology]; observables; quantum cosmology; statistical mechanics.
* Idea: The spacetime manifold remains, although one sometimes considers contributions from different ones.
* Status: 1988, Most results have come just from quantum field theory in curved spacetime calculations; The next step is to include the back-reaction, necessary to achieve above goals and to understand things like dissipation of anisotropies.
* Perturbative: The fuzziness in the metric and causal relations is obtained by quantizing deviations from a background, reference metric, usually taken to be flat or (anti-)de Sitter, on a fixed manifold; Initially based on the Lorentz-covariant spin-2 field theory in 4D Minkowski (possibly including higher-derivative theories or supergravity, and/or using path integrals), and thus called "covariant quantum gravity"; It is the approach that has been most used in combination with other interactions, and later merged in part with superstrings/M-theory;
* Non-perturbative: (i) Canonical approach, including spin networks; (ii) Asymptotic quantization (see below); (iii) Path integral quantization (Lorentzian or Euclidean), including spin foams; (iv) Numerical approach by lattice gravity or Regge calculus; (v) Stochastic quantization.
@ General references: Flori a0911-PhD [loop quantum gravity and topos theory].
@ Perturbative: Mandelstam AP(62), PR(68); Floreanini & Percacci PRD(92) [mean-field approach]; Tsamis & Woodard AP(95) [strong infrared effects]; Parentani NPB(97)gq/96 [radiative processes in quantum cosmology]; Ichinose & Ikeda IJMPA(99)ht/98; Deser AdP(99)gq/99 [infinities, including supergravity]; Bern LRR(02) [relationship with gauge theory]; Tsuneyama ht/04/PRD; Freidel & Starodubtsev ht/05 [topological field theory approach]; Brunetti & Fredenhagen gq/06-in [background-independent]; Anselmi & Benini JHEP(07)-a0704 [higher-derivative corrections]; Bern et al PRD(08)-a0707 [unexpected cancellations]; Ward IJMPD(08) [resummed]; > s.a. friedmann equation [quantum corrections].
> Various approaches: see canonical and covariant quantum gravity; Dirac Sea; effective theories; lattice gravity [including regge calculus]; modified theories [including linearized and category-based]; path-integral quantization; Quaternions; semiclassical general relativity; string theory.

Other Approaches > s.a. decomposition; holography; spacetime topology; stochastic quantum mechanics; teleparallel gravity.
@ Affine quantization: Klauder JMP(99)gq, JMP(01)gq, CQG(02)gq/01, IJMPD(03)gq; Watson & Klauder JMP(00)qp, CQG(02)gq/01; Klauder gq/04-in, gq/04-in, IJGMP(06), JPCS(07)gq/06, a0711-in.
@ Conformal factor: Padmanabhan PRD(83), PRD(83); Bleecker CQG(87); Floreanini & Percacci NPB(95) [effective potential]; Antoniadis et al PRD(97)ht/95, PRD(97)ht/95; in Burdet & Perrin gq/97; Shojai et al MPLA(98)gq/99; Shojai IJMPA(00)gq [??].
@ Metric uncertainty: Diósi & Lukács PLA(89); Maggiore PLB(93)ht.
@ Covariant Hamiltonian: Kanatchikov gq/98-in, gq/99, IJTP(01)gq/00 [de Donder-Weyl]; Aleksandrov TMP(04) [covariant lqg].
@ As theory of embeddings: Pavsic FP(96)gq/95, G&C(96)gq/95; Hájícek & Kiefer NPB(01)ht/00 [spherical shell].
@ And spinor fields: Lisi gq/02; Galehouse in(04)mp/02; Kober PRD(09)-a0812; > s.a. canonical quantum gravity; spin networks.
@ Quasilocal: Conrady et al PRD(04)gq/03 [vacuum].
@ Group field theory: Oriti JPCS(06)gq/05, in(09)gq/06; Freidel IJTP(05)ht; Ryan gq/06 [new proposal]; Oriti JPCS(07)ht/06, a0709-in, a0710-in; Oriti & Tlas CQG(08)-a0710 [unifying framework for lqg and simplicial quantum gravity]; Oriti a0902 [and simplicial quantum gravity], JPCS(09)-a0903; > s.a. deformed special relativity.
@ Based on fluctuations: Zakir ht/98, ht/99; Hu IJTP(02)gq [kinetic theory of fluctuations]; Hall GRG(05) [from "exact uncertainty"]; > s.a. quantum spacetime; stochastic quantization.
@ Emergent, condensate: Hu gq/06-in [and stochastic gravity]; Hedrich a0902; > s.a. gravity theories.
@ Newtonian: Hansson gq/06; Bramson PRS(07) [axisymmetric, spinning systems].
@ Asymptotic safety: Weinberg in(79); Reuter & Schwindt JPA(07)ht/06, JHEP(07) [scale-dependent metric and minimum length]; Percacci in(09)-a0709 [rev]; Benedetti et al a0901 [for higher-derivative gravity]; Manrique & Reuter a0907 [background metric]; Benedetti et al a0909-in [role of higher-derivative terms]; Bonanno a0911-in [astrophysical implications]; > s.a. renormalization.
@ Other: Banks NPB(85); Gotay CQG(86); Casher PLB(87); Kleinert PLB(87); Kocharovsky & Kocharovsky FP(87); Kiefer PLA(89) [analogy with brownian motion]; Balbinot et al PRD(90) [and adiabatic phase]; Myers CQG(92) [unbounded action]; Greensite PRD(94)gq/93 [transfer matrix formalism]; Galehouse qp/94; Crane JMP(95)gq [algebraic]; Modanese NPB(95) [potential energy]; Prugovecki in(96)gq/95 [quantum frame bundles]; Federbush ht/99; Kanatchikov gq/00-in, IJTP(01)gq/00 [precanonical]; Dzhunushaliev & Singleton Ent(02)gq/01 [and complexity]; Nishikawa ht/02-in [minimal assumptions]; Minic & Tze PLB(04)ht/03, ht/04-in; Moffat gq/04 [in momentum space]; Jejjala et al IJMPD(04)gq [??]; Krasnov ht/06 [non-metric, renormalizable]; Iftime DGDS-gq/07; Nassif a0709 [at large length scales]; Finkelstein IJTP(08) [homotopy]; Glinka G&C-a0808; Darabi a0809 [phenomenological].

Asymptotic Quantization
* At null infinity: It lies somewhere in between the canonical approach and the covariant one; One avoids the 3+1 decomposition of the former and the linearization and use of a fixed background of the latter, and quantizes the radiation degrees of freedom (idea taken from QED), using the asymptotic properties of the gravitational field.
@ Null surfaces formulation: Frittelli et al PRD(97)gq/96; Domínguez & Tiglio PRD(99)gq [large effects].
@ At null infinity: Ashtekar PRL(81), JMP(81), in(81), 87.
@ At spatial infinity: Alexander & Bergmann FP(84) [electromagnetism], FP(86); Bergmann GRG(87), GRG(89).


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