Quantum
Regge Calculus| Quantum
Regge Calculus |
In General > s.a. lattice
field theory; models of topology
change;
[quantum gravity, quantum
spacetime].
* Features: Non-perturbative; 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.
* And spin foam: The large spin asymptotics of the Barrett-Crane vertex amplitude
is known to be related to the Regge action.
References > s.a. dynamical triangulations;
einstein-cartan theory.
@ General: Rocek & Williams in(82); Hamber in(84), in(86); Hartle
in(85), in(86); Schleich in(94); Immirzi CQG(96)gq/95.
@ Intros, reviews: in Isham in(86); de Bakker hl/95-PhD;
Williams NPPS(97)gq;
Ambjørn et al ht/00, gq/02-in;
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 [
area
],
gq/03, PLB(04)gq [length].
@ 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 measure].
@ Diffeomorphism invariance: Hartle JMP(85);
Lehto et al NPB(86);
Pfeiffer PLB(04)gq/03 [and
local degrees of freedom].
@ Propagators: Rocek & Williams PLB(81),
ZPC(84); Feinberg
et al NPB(84); Williams CQG(86).
@ 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-in.
@ 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].
@ 2D, measure: Menotti & Peirano NPB(96)ht;
Nieto PLB(05)hl;
Zubkov PLB(05).
@ 3D:
Ambjørn et al PRL(00)ht, PRD(01)ht/00 [Lorentzian
path integral];
> s.a. 3D geometries, 3D
quantum gravity.
@ Higher-dimensional:
Hamber & Williams PRD(06)ht/05 [large-D limit].
@ 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.
@ 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]; Ambjørn et al PRL(05)ht [short-distance
2-dimensionality]; Khatsymovsky PLB(07)gq/06 [possible
finiteness of theory]; Dittrich et al PRD(07)
[4-simplex action and linearized quantum gravity]; Bianchi & Modesto NPB(08)-a0709
[and spin foam].
@ Numerical: Berg PRL(85); Hartle pr(86); Hamber gq/98 [custom-built
supercomputer].
Semiclassical
@ References: 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].
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