Approaches
to Quantum Gravity| Approaches
to Quantum Gravity |
In General, "Conventional" Approaches > s.a.
[quantum gravity, phenomenology]; observables; 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, 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, including spin networks; (ii) Asymptotic (see below); (iii) Path
integral (Lorentzian
or Euclidean), including spin foams; (iv) Numerical approach by lattice
gravity or Regge calculus; (v) Stochastic.
@ Perturbative: Mandelstam AP(62),
PR(68);
Floreanini & Percacci PRD(92)
[mean field approach]; Tsamis & Woodard AP(95)
[strong ir 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];
Tsuneyama ht/04/PRD;
Freidel & Starodubtsev ht/05 [topological
field theory approach]; Brunetti & Fredenhagen gq/06-in
[background-independent]; Anselmi & Benini a0704 [higher-derivative
corrections]; Bern et al a0707 [unexpected
cancellations]; Ward IJMPD(08)
[resummed].
> Various approaches:
see canonical, covariant, Dirac
Sea, effective theories, lattice
gravity [including regge calculus], modified
theories [including linearized], path integral
quantization, semiclassical general relativity,
and string
theory.
References > s.a. decomposition;
quantum cosmology; spacetime
topology; stochastic
quantum mechanics; teleparallel.
@ 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),
gq/06-in,
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: Garrett gq/02;
Galehouse in(04)mp/02; > s.a. canonical
quantum gravity, spin networks.
@ Holographic: Smolin PRD(00)ht/98;
Balasubramanian & Kraus PRL(99)ht.
@ Quasilocal: Conrady et al PRD(04)gq/03 [vacuum].
@ Group field theory:
Oriti gq/04-in, gq/06-in;
Freidel IJTP(05)ht;
Ryan gq/06 [new
proposal]; Oriti ht/06-in,
a0709-in,
a0710-in; Oriti
& Tlas CQG(08)-a0710 [unifying
framework for lqg and simplicial quantum gravity].
@ Based on fluctuations: Zakir ht/98, ht/99;
Hu IJTP(02)gq [kinetic
theory of fluctuations]; Hall GRG(05)
[from "exact uncertainty"]; Hu gq/06-in
[condensate and stochastic gravity]; > s.a. quantum
spacetime, stochastic quantization.
@ Newtonian: Hansson gq/06; Bramson
PRS(07) [axisymmetric, spinning systems].
@ Asymptotic safety: Weinberg in(79); Reuter & Schwindt ht/06-in, JHEP(07), JPA(07)
[scale-dependent metric and minimum length]; Percacci a0709-in [rev]; > 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 gq/07; Nassif a0709 [at
large length scales]; Finkelstein IJTP(08)
[homotopy].
Approaches Based on Different Frameworks > s.a. non-commutative
geometry, quantum
spacetime, Topos
Theory.
* Possibilities:
Modify the underlying structure, such as (i) Twistors; (ii) Algebraic approaches,
quantum groups, non-commutative geometry; (iii) Finkelstein and other fundamentally
quantum approaches (plexars, quantum topology); (iv) Posets, as finite spatial
topologies, or as causal sets; (v) Fundamentally discrete approaches.
@ From space of histories: DeWitt & Molina-Paris MPLA(98)ht.
@ Bohm / pilot wave: Shtanov PRD(96)gq/95;
Goldstein & Teufel qp/99-in;
Shojai PRD(99)gq, & Golshani
IJMPA(98), IJMPA(98)gq/99, & Shojai
CQG(04)gq/03;
Santini gq/00-PhD
[canonical quantum gravity]; Pinto-Neto & Santini GRG(02);
Kenmoku et al CQG(02)
[3D spherical];
Shojai & Shojai gq/04-in
[lqg]; Shojai et al IJMPA(05)gq
[Einstein universe]; Carroll TMP(07)
[fluctuations and entropy]; > s.a. canonical
quantum gravity.
@ And other hidden variables: 't Hooft CQG(99)gq [information
dissipation].
@ And spectral geometry: Esposito 98-ht/97, ht/97-in,
CM(05)ht/03-in
[Euclidean]; Booss-Bavnbek et al Sigma(07)-a0708 [rev];
Kempf & Martin a0708 [information theory and cutoffs].
@ Causality-based: Schorn CQG(97), CQG(97);
Rainer IJTP(00)gq/97, CQG(00)gq/99 [algebraic];
Hardy gq/05,
JPA(07)gq/06-in,
a0804-in
["causaloids"];
Christensen & Crane JMP(05)
[causal sites]; > s.a. causal sets.
@ Discrete: Holfter & Paschke JGP(03)ht/02 [and
Dirac operator]; Gambini & Pullin gq/05-in; > s.a. discrete
spacetime.
@ Categorical: Crane ht/93, gq/00;
Isham ATMP(03)gq,
ATMP(03)gq,
ATMP(04)gq/03;
Baez qp/04;
Raptis IJTP(06)gq/04-in,
IJTP(07)
[and abstract differential geometry];
Crane gq/06-in.
@ Relational: Corichi et al MPLA(02)gq;
Dreyer gq/04;
Raptis IJTP(07)
['third
quantization']; Dreyer a0710-in
[internal relativity].
@ Deformed: Finkelstein LMP(96);
Antonsen gq/97;
Gavrilik gq/99-in
[quantum algebras]; Vacaru a0801 [Lagrange-Finsler
variables and Fedosov quantization]; > s.a. loop
representation, modified
theories [linearized gravity], modified versions
of general relativity.
@ Related topics: Ghosh
ht/02 [use
all signatures]; Siino ht/06 [algebraic];
Finkelstein gq/06/IJTP
[homotopy approach]; Raptis IJTP(06)
[Glafka meeting, iconoclastic approaches].
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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Send feedback and suggestions to bombelli at olemiss.edu – Modified
11 jul 2008