Approaches to Quantum Gravity  

In General > s.a. quantum gravity [overviews]; observables; phenomenology; quantum cosmology; semiclassical general relativity; statistical mechanics.
* Main types: One may distinguish between (a) "conventional" approaches, which can be based on the quantization of a classical gravity theory (quantum geometrodynamics, loop quantum gravity, spin-foam models, Regge calculus and causal dynamic triangulations, group field theory) or on an extension of quantum field theory (string theory), and (b) other approaches, often discrete, sometimes combinatorial or based on condensed-matter physics ideas (causal sets, quantum graphity).
* "Conventional" approaches: The spacetime manifold remains, although one sometimes considers contributions from different ones; 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, Regge calculus, or dynamical triangulations; (v) Stochastic quantization.
@ Perturbative: Mandelstam AP(62), PR(68); Floreanini & Percacci PRD(92) [mean-field approach]; 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)gq [relationship with gauge theory]; Tsuneyama ht/04/PRD; Freidel & Starodubtsev ht/05 [topological field theory approach]; Brunetti & Fredenhagen gq/06-proc [background-independent]; Anselmi & Benini JHEP(07)-a0704 [higher-derivative corrections]; Bern et al PRD(08)-a0707 [unexpected cancellations]; Ward IJMPD(08) [resummed]; Benedetti & Speziale JHEP(11)-a1105 [1st-order tetrad formalism and Immirzi parameter]; Vereshkov & Marochnik JModP(13)-a1108 [Heisenberg representation]; Akhoury et al PRD(11) [collinear and soft divergences]; Hossenfelder PLB(13)-a1208 [as an effective theory]; Brunetti et al a1306 [as a locally covariant quantum field theory]; Upadhyay PLB(13)-a1305 [Batalin-Vilkovisky formalism], EPJC(14)-a1312 [gaugeon formalism]; Huang a1312 [in imaginary time]; Bellazzini et al PRD(16)-a1509 [constraints from unitarity and analyticity]; > s.a. covariant quantum gravity [including infrared behavior]; friedmann equation [quantum corrections].
@ Non-perturbative: Ambjørn et al PRP(12)-a1203 [CDT, asymptotic safety, lattice gravity].
@ And topos theory: Flori PhD(09)-a0911, Dahlen a1111 [loop quantum gravity]; Döring a1306 [and neo-realist interpretation].

blue bullet "Conventional" approaches: see canonical [including affine] and covariant quantum gravity; effective theories; higher-order gravity; lattice gravity and regge calculus; modified theories [including linearized, higher-dimensional, deformed, category-based, pilot-wave, simplified models]; path-integral quantization; string theory.

Other Approaches > s.a. emergent gravity; physical theories; non-commutative gravity; spacetime topology; stochastic quantum mechanics; quaternions.
@ 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 [??]; 't Hooft a1009 [integrating over the conformal factor first]; Hamada PRD(12).
@ Metric uncertainty: Diósi & Lukács PLA(89); Álvarez et al PRD(92) [quantum metric space]; Maggiore PLB(93)ht; Chiang et al PRD(16)-a1512 [spacetime interval operator].
@ Covariant Hamiltonian: Kanatchikov gq/98-proc, gq/99, IJTP(01)gq/00 [de Donder-Weyl]; Aleksandrov TMP(04) [covariant lqg].
@ As theory of embeddings: Pavšič CQG(85)-a1403, FP(96)gq/95, G&C(96)gq/95; Hájíček & Kiefer NPB(01)ht/00 [spherical shell].
@ And spinor fields: Lisi gq/02; Galehouse in(04)mp/02; Kober PRD(09)-a0812; Hughes & Randono a1105 [is geometry bosonic or fermionic?]; Vladimirov & Diakonov PRD(12)-a1208 [phase transitions in spinor quantum gravity on a lattice]; > s.a. canonical quantum gravity; spin networks.
@ Local: Noldus a1101; Larsson a1407 [diffeomorphism symmetry, unitarity, and locality postulated].
@ 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-proc, a0710-proc; Oriti & Tlas CQG(08)-a0710 [unifying framework for lqg and simplicial quantum gravity]; Oriti CQG(10)-a0902 [and simplicial quantum gravity], JPCS(09)-a0903; Oriti & Tlas CQG(10)-a0912 [simplicial quantum geometry]; Oriti a0912-proc [rev]; Oriti & Sindoni NJP(11)-a1010-in [hydrodynamics, and classical geometrodynamics]; Vitale PoS-a1103 [relationship with discretized BF models]; Livine et al CQG(11)-a1104 [and the canonical Hamiltonian constraint]; Oriti a1110-ch [introduction]; Baratin & Oriti JPCS(12)-a1112 [non-technical]; Vitale AIP(12)-a1203 [rev]; Gielen et al PRL(13)-a1303 [cosmology]; Oriti CQG(16)-a1310 & CQG+ [as the 2nd quantization of lqg]; Calcagni PRD(14)-a1407 [and lqc]; Oriti a1408-in [and lqg]; Oriti et al NJP(15)-a1409 [for the whole loop quantum gravity state space]; Carrozza PRD(15)-a1411 [in dimension 4 – ε]; > s.a. deformed special relativity; renormalization.
@ Group field theory, quantum cosmology: Gielen & Sindoni Sigma(16)-a1602; Gielen CQG(16)-a1604 [from GFT condensate]; de Cesare et al a1606 [cyclic universe and accelerated expansion]; Oriti a1612-CRP [intro].
@ Group field theory, with matter: Li et al a1703 [scalar field].
@ Based on fluctuations: Zakir ht/98, ht/99; Hu IJTP(02)gq [kinetic theory of fluctuations]; Hall GRG(05) [from "exact uncertainty"]; Succi IJMPC(12)-a1111 [Kolmogorov scaling theory, turbulence, and fractal spacetime]; > s.a. quantum spacetime; stochastic quantization.
@ Newtonian: Hansson PE(10)gq/06; Bramson PRS(07) [axisymmetric, spinning systems].
@ Algebraic methods: Crane JMP(95)gq; Tanasa CQG(10)-a0909; Martins IJMPA(13)-a1003 [overview]; Etesi a1402 [and orientation-preserving diffeomorphism group]; Giddings JHEP(15)-a1503 [Hilbert space structure, non-locality and entanglement]; Araya-Gochez a1601 ["quantum ring theory"]; Rejzner a1603-conf [perturbative].
@ Analog models: Kiefer PLA(89) [analogy with brownian motion]; Baker a0810 [elastic-solid model]; Krein et al PRL(10)-a1006 [phonons in random fluids].
@ Renormalizable theory proposals: Krasnov ht/06 [non-metric]; Wiesendanger JModP(14)-a1308 [gauge theory of volume-preserving diffeomorphisms].
@ And gauge theory: Ragiadakos a1204-GRF [Lorentzian complex structure of spacetime]; Hanada a1407-conf [gauge/gravity duality and super Yang-Mills theory]; > s.a. covariant quantum gravity.
@ Discretized models: Hamma & Markopoulou NJP(11)-a1011 [condensed-matter-type spin models]; Gudder a1109-wd; Rivasseau AIP(12)-a1112, a1209-conf, a1311, FdP-a1406-proc, a1604-proc [tensor-track approach, including a sum over all topologies]; > s.a. discrete geometries; quantum spacetime.
@ Information-based: Mandrin a1408, a1409, a1411 [from minimum information]; Chen a1412 [informationally-complete unification].
@ Precanonical quantization: Kanatchikov NPPS(00)gq, IJTP(01)gq/00, AIP(13)-a1212, NPCS-a1407, a1512-MG14; > s.a. approaches to canonical qg.
@ Related topics: Banks NPB(85); Gotay CQG(86); Casher PLB(87); Kleinert PLB(87); Kocharovsky & Kocharovsky FP(87); Balbinot et al PRD(90) [and adiabatic phase]; Myers CQG(92) [unbounded action]; Greensite PRD(94)gq/93 [transfer matrix formalism]; Galehouse qp/94; Modanese NPB(95) [potential energy]; Prugovečki in(96)gq/95 [quantum frame bundles]; Schmelzer gq/98 [condensed-matter type]; Federbush ht/99; Dzhunushaliev & Singleton Ent(02)gq/01 [and complexity]; Nishikawa ht/02-conf [minimal assumptions]; Minic & Tze PLB(04)ht/03, ht/04-proc; Moffat gq/04 [in momentum space]; Jejjala et al IJMPD(04)gq [??]; Iftime DGDS-gq/07; Nassif a0709 [at large length scales]; Finkelstein IJTP(08) [homotopy]; Glinka G&C(10)-a0808; Darabi a0809 [phenomenological]; Yang MPLA(10)-a1007; Yang a1111-proc ["background-independent"]; Takook & Rouhani a1208 [Krein space quantization]; Palmer a1210 ["gravitational theory of the quantum"]; Bastianelli & Bonezzi a1304 [worldline approach]; news ns(13)may [Weinstein's theory of everything]; Salvio & Strumia JHEP(14)-a1403 [without scales, "agravity"]; Sutherland a1502 ["naive", using final boundary conditions]; Mandrin a1505 [non-dynamical approach, NDA]; Walstad a1507 [from special relativity and quantum theory]; Olmo & Rubiera-García IJMPD(15)-a1507 [point defects and dislocations desctibed by non-metricity and torsion]; Spaans 15 [based on paths]; Horndeski a1508 [with gravitons as holes in space]; Arbuzov et al a1511 [Von Neumann's procedure]; > s.a. decomposition; Dirac Sea; duality [gauge/gravity, surface-state]; holography; renormalization and asymptotic safety; Third Quantization.

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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