Approaches
to Quantum Gravity| 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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