Discretized / Lattice Gravity  

Classical Versions > s.a. gravity theories / discrete geometry; semiclassical quantum gravity [twisted geometry]; teleparallel gravity; {& DeWitt}.
* Idea: The best-known version is Regge calculus, in which the discrete structure is a simplicial complex and the variables are its edge lengths; One variant is dynamical triangulations, in which all edge lengths are taken to be unit, and there is also a version in which the variables are areas; A less rigid piecewise-flat geometry is twisted geometry.
@ General references: Lindquist & Wheeler RMP(57); Brewin CQG(98)gq/97 [ADM].
@ Connection / triad variables: Boström et al gq/93 [discretization]; Dupuis et al a1701 [different polarizations]; > s.a. connection formulation.
@ Triangulations, simplices: Ko & Roček JHEP(06)ht/05, ht/06-conf [effective action and variation]; Lee IJMPA(09)gq/06 [emergence]; Dittrich & Ryan CQG(11)-a0807, PRD(10) [phase-space descriptions]; Yukawa PRD(11)-a1104 [master equation for Markov process of a 2D spacetime lattice]; Dittrich & Höhn CQG(12)-a1108 [canonical simplicial gravity]; Khatsymovsky GRG(11); Höhn JPCS(12)-a1110 [canonical formalism, rev]; Wieland CQG(15)-a1407 [4D, new action, with spinors as fundamental variables]; > s.a. first-order actions for general relativity; regge calculus.
@ Consistent discretizations: Gambini & Pullin gq/01-in, GRG(05)gq-GRF [classical and quantum]; Bahr et al PRD(11)-a1101 [discretizations and reparametrization invariance]; Brewin PRD(12)-a1104 [Einstein-Bianchi system].
@ Other discretizations: de Albuquerque et al PRL(03)ht, MPLA(03)ht-conf [Euclidean, non-commutative spectral principle dynamics]; Gambini & Pullin in(05)gq, IJMPD(06)gq/05-proc; Gambini & Pullin CQG(08)-a0807 [uniform discretizations].
@ Specific spacetimes: Brewin & Kajtar PRD(09)-a0903 [Oppenheimer-Snyder]; Brewin PRD(17)-a1703 [Cauchy evolution of Gowdy, Brill and Teukolsky initial data].
@ 3D (2+1 dimensions): Waelbroeck CQG(90) [from the Chern-Simons formulation of 2+1 gravity]; Criscuolo & Waelbroeck gq/96 [constant curvature]; Berra-Montiel & Rosales-Quintero IJMPA(15)-a1406 [with cosmological constant, canonical analysis].
@ Continuum limit: Feinberg et al NPB(84) [and fundamental nature].
@ Related topics: Wheater JPA(94) [random surfaces and strings in various dimensions]; Gionti CQG(05)gq [Poincaré-invariant, first-order].

Quantum versions > s.a. canonical quantum gravity; discrete spacetime models; quantum regge calculus; spin-foam models; spin networks.
@ Reviews: Loll gq/97-conf, LRR(98)gq; Loll NPPS(01)ht/00 [lorentzian]; Hamber GRG(09)-a0901; Ambjørn et al PoS-a1105 [specially dynamical triangulations].
@ Connection / loop representation: Loll ACosm(95)gq, NPPS(97)gq, proc(97)gq; Loll CQG(98)gq/97 [algebra of diffeomorphism constraints]; Fort et al PRD(97)gq/96.
@ Consistent discretization: Gambini & Pullin PRL(03)gq/02 [canonical formalism], CQG(03)gq/02 [and cosmology], Pra(04)gq, gq/04-proc [canonical quantum gravity].
@ Continuum limit: Vergeles ht/06, JETP(13) [and state doubling problem]; Hamber et al PRD(12)-a1212 [triangulation version of the Wheeler-DeWitt equation, vacuum state].
@ Euclidean: Krzywicki APPB(96)hl/95 [rev]; Catterall et al EPJP(12)-a0912 [and de Sitter space].
@ Diffeomorphism invariance: Corichi & Zapata NPB(97)gq/96; Wetterich LNP(13)-a1201.
@ Related topics: Greensite PLB(91) [minimum length from lattice regularization]; Malyshev RMS(01)gq [and Gibbs measure]; Wetterich PLB(11)-a1108, AP(12)-a1201 [in terms of fermions]; Cooperman a1410 [renormalization]; Hamber PRD(15)-a1506 [scaling exponents]; Mandrysz & Mielczarek a1804 [ultralocal phase transition]; Majid a1810 [on a square graph].

Other Theories > s.a. discrete geometries; graph theory in physics; lattice field theory and gauge theory.
@ References: Zubkov PLB(04)hl/03 [teleparallel gravity].

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