Approaches to Quantum Gravity |

**In General** > s.a. 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.

@ __General references__:
Mielczarek & Trześniewski GRG(18)-a1708 [links between approaches];
> s.a. quantum gravity [overviews].

**Perturbative Approaches** > s.a. covariant quantum gravity;
renormalization; string theory.

* __Idea__:
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.

@ __General references__:
Deser AdP(99)gq/99 [infinities, including supergravity];
Anselmi & Benini JHEP(07)-a0704 [higher-derivative corrections];
Bern et al PRD(08)-a0707 [unexpected cancellations];
Ward IJMPD(08) [resummed];
Akhoury et al PRD(11) [collinear and soft divergences];
Bellazzini et al PRD(16)-a1509 [constraints from unitarity and analyticity];
Anselmi a1909 [proof of perturbative unitarity];
> s.a. covariant quantum gravity [including infrared behavior];
friedmann equation [quantum corrections].

@ __Versions__: Mandelstam AP(62),
PR(68);
Floreanini & Percacci PRD(92) [mean-field approach];
Ichinose & Ikeda IJMPA(99)ht/98;
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];
Benedetti & Speziale JHEP(11)-a1105 [1st-order tetrad formalism and Immirzi parameter];
Vereshkov & Marochnik JModP(13)-a1108 [Heisenberg representation];
Hossenfelder PLB(13)-a1208 [as an effective theory];
Brunetti et al CMP(16)-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];
Barvinsky et al PRD(18)-a1806 [Correlated Worldline theories].

@ __With matter__: Prinz a1812 [spinor electrodynamics].

@ __Applications__: Parentani NPB(97)gq/96 [radiative processes in quantum cosmology].

**Non-Perturbative Approaches**
> s.a. canonical quantum gravity [including affine, lqg];
path-integral quantization; renormalization.

* __Idea__: (i) Canonical
approach, including spin networks; (ii) Asymptotic quantization; (iii) Path
integral quantization (Lorentzian or Euclidean), including spin foams; (iv)
Numerical/discrete approaches auch as lattice gravity, Regge calculus,
causal sets or dynamical triangulations; (v) Stochastic quantization.

@ __ References__: Ambjørn et al PRP(12)-a1203 [CDT, asymptotic safety, lattice gravity];
Tavernelli a1801 [based on a geometrization of quantum mechanics];
Giddings FP(19)-a1803,
a1805 [intrinsically quantum approach].

@ __And topos theory__: Flori PhD(09)-a0911,
Dahlen a1111 [loop quantum gravity];
Döring a1306 [and neo-realist interpretation].

**Discrete Approaches** > s.a. causal sets;
discrete spacetime models [including quantum graphity];
lattice gravity and regge calculus.

@ __ References__: Schmelzer gq/98 [condensed-matter type];
Holfter & Paschke JGP(03)ht/02 [and Dirac operator];
Gambini & Pullin in(09)gq/05;
Hamma & Markopoulou NJP(11)-a1011 [condensed-matter-type spin models];
Gudder a1109-wd;
Rivasseau AIP(12)-a1112,
a1209-conf,
FdP(14)-a1311,
FdP(14)-a1406-proc,
a1604-proc
[tensor-track approach, including a sum over all topologies];
Oriti a1710-fs
[spacetime as a quantum many-body system];
Majid a1810 [on a square graph];
Eichhorn et al a1811 [tensor models];
> s.a. quantum spacetime.

@ __Information-based__: Mandrin a1408,
a1409,
a1411 [from minimum information];
Chen a1412
[informationally-complete unification].

**Asymptotic Quantization**

* __At null infinity__: It
lies somewhere 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).

**Other Approaches** > s.a. effective theories;
observable algebras; types of approaches
[including group field theory]; interpretations of quantum mechanics.

@ __Other dimensions__: Bjerrum-Bohr NPB(04)ht/03 [*D* → ∞];
Nieto a0704
[8D, background-independent Kaluza-Klein à la lqg];
Nieto RMF-a1003 [8D and (2+2) loop quantum gravity],
IJGMP(12)-a1107 [in 2+2 dimensions];
Vaugon a1512
[pure geometry, of signature (–, –, +, ..., +)];
Deser GRG(16)-a1609 [1-loop divergences cannot all be removed in *D* > 4];
> s.a. 2D and 3D quantum gravity;
regge calculus.

@ __Using condensed matter ideas__:
Olmo & Rubiera-García IJMPD(15)-a1507
[point defects and dislocations described by non-metricity and torsion].

@ __Based on paths__: Bastianelli & Bonezzi a1304 [worldline approach]; Spaans 15 [based on paths]; > s.a. world function.

@ __Analog models__: Kiefer PLA(89) [analogy with brownian motion];
Baker a0810 [elastic-solid model];
Krein et al PRL(10)-a1006 [phonons in random fluids].

@ __Categorical__: Crane ht/93,
gq/00;
Isham ATMP(03)gq,
ATMP(03)gq,
ATMP(04)gq/03;
Isham FP(05)qp/04-in;
Baez qp/04;
Raptis IJTP(06)gq/04-conf,
IJTP(07) [and abstract differential geometry];
Crane gq/06-ch;
> s.a. categories in physics; quantum
spacetime models; Topos Theory.

__Based
on modified gravity__: see higher-order gravity; modified approaches
[including linearized, deformed, pilot-wave, simplified models].

main page
– abbreviations
– journals – comments
– other sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 14 sep 2019