Quantum Regge Calculus| Quantum Regge Calculus |
In General
> s.a. quantum gravity; quantum spacetime
/ lattice field theory; lattice
gravity; models of topology change.
* Idea: A non-perturbative
approach to discrete quantum gravity, based on simplices and metric variables;
Exhibits a short-range non-locality.
* Status: 2001, After a lot
of work on the question of phase transitions, it is generally believed
that the standard version with continuous edge lengths is not viable
because it only has a first-order phase transition, and comes to be
dominated by a crumpled phase; This motivates the dynamical triangulations
approach, or the use of a different set of variables.
@ General references:
Roček & Williams PLB(81),
in(82);
Hamber in(84),
in(86);
Hartle in(85),
in(86);
Schleich in(94);
Immirzi CQG(96)gq/95;
Hamber & Williams PRD(11)-a1109 [discrete Wheeler-DeWitt equation];
Tate & Visser JHEP(11)-a1108 [Lorentzian-signature model].
@ Intros, reviews: in Isham in(86);
de Bakker PhD(95)hl;
Williams NPPS(97)gq;
Ambjørn et al ht/00;
Ambjørn gq/02-GR16;
Khatsymovsky JETP(05)gq;
Loll et al CP(06)ht/05 [causal dynamical triangulations].
@ Sum over histories: Lehto et al CMP(84),
NPB(86),
NPB(87) [euclidean];
Jevicki & Ninomiya PRD(86);
Römer & Zähringer CQG(86) [gauge fixing];
Schleich & Witt NPB(93)gq,
NPB(93)gq [sum over topologies];
Khatsymovsky PLB(03)gq/02 [\(\langle\)area\(\rangle\)],
gq/03,
PLB(04)gq [\(\langle\)length\(\rangle\)];
Khatsymovsky MPLA(10)-a1005 [integration over connections];
Dittrich et al CQG(14)-a1404 [discretization independence and non-locality];
Marzuoli & Merzi IJGMP(16)-a1601;
Miković & Vojinović a1804-proc;
Miković a2001 [piecewise flat metrics].
@ Sum over histories, area Regge calculus: Khatsymovsky PLB(04)gq,
PLB(04)gq,
PLB(06)gq/05 [Lorentzian],
PLB(06)gq/06 [euclidean],
a0707 [positivity of the measure].
@ Measure: Hartle JMP(85);
Bander PRL(86);
Khatsymovsky CQG(94)gq/93;
Menotti & Peirano NPPS(97)gq;
Hamber & Williams PRD(99)ht/97 [standard vs non-local];
Khatsymovsky PLB(01) [Faddeev-Popov factor],
PLB(02)gq/01,
PLB(04)gq;
Gambini & Pullin IJMPD(06) [from consistent discretization].
@ Diffeomorphism invariance: Hartle JMP(85);
Lehto et al NPB(86);
Pfeiffer PLB(04)gq/03 [and local degrees of freedom].
@ Propagators:
Roček & Williams PLB(81),
ZPC(84);
Feinberg et al NPB(84);
Williams CQG(86).
Types of Models and Relationships > s.a. cosmological-constant
problem; dynamical triangulations; einstein-cartan theory.
* And spin-foam approach:
The large-spin asymptotics of the Barrett-Crane vertex amplitude is known
to be related to the Regge action.
@ In quantum cosmology: Birmingham PRD(95)gq [lens space];
Correia da Silva & Williams CQG(99)gq [with scalar],
CQG(99)gq [anisotropic].
@ Minisuperspace: Hartle JMP(85),
JMP(86),
JMP(89);
Louko & Tuckey CQG(92);
Furihata PRD(96) [no-boundary, anisotropic + cosmological constant];
Birmingham GRG(98)gq/97 [cone on a space];
Correia da Silva & Williams CQG(00)gq [+ massive scalar],
gq/00/CQG [wormholes].
@ And matter: Drummond NPB(86);
Ren NPB(88);
Hamber & Williams NPB(94) [scalar, effect on phase transition];
Ambjørn et al JHEP(99)hl [abelian gauge theory];
Gionti gq/06-proc;
Paunković & Vojinović JPCS-a1601 [gravity-matter entanglement].
@ 2D: Menotti & Peirano NPB(96)ht,
Nieto PLB(05)hl,
Zubkov PLB(05) [measure];
Yukawa PRD(12) [as Markov process, master equation].
@ 3D: Ambjørn et al PRL(00)ht,
PRD(01)ht/00 [Lorentzian path integral];
> s.a. 3D geometries; 3D quantum gravity.
@ 4D: Höhn PRD(15)-a1411 [canonical, linearized Regge calculus and lattice gravitons].
@ Higher-dimensional: Hamber & Williams PRD(06)ht/05 [large-D limit].
@ Semiclassical: Barrett & Faxon CQG(94)gq/93;
Demkin MPLA(00) [simplicial complexes];
Ambjørn et al PLB(05)ht/04,
PRD(05)ht [from causal dynamical triangulations];
Bianchi & Satz NPB(08)-a0808 [and spin foams].
@ Phase transitions: Ambjørn et al PLB(92),
Ambjørn & Varsted NPB(92) [3D, euclidean];
Hamber & Williams PRD(93),
Hamber NPB(93) [critical exponents];
Ambjørn & Jurkiewicz NPB(95)ht;
> s.a. regge calculus.
@ And spin-foam approach:
Bianchi & Modesto NPB(08)-a0709;
Gionti IJGMP(12)-a1110-proc;
> s.a. spin-foam quantum gravity.
@ Numerical: Berg PRL(85);
Hartle pr(86);
Hamber gq/98 [custom-built supercomputer].
@ Related topics: Brügmann & Marinari PLB(95)ht/94 [exponential bound];
Hamber & Liu NPB(96)ht [perturbative, Feynman rules];
Ambjørn et al CQG(97)gq [spikes];
Bilke & Thorleifsson NPPS(99)hl/98,
PRD(99)hl/98 [degenerate triangulation];
Khatsymovsky PLB(07)gq/06 [possible finiteness of theory];
Dittrich et al PRD(07) [4-simplex action and linearized quantum gravity].
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