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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