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].

__"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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jun 2017