Discretized / Lattice Gravity| 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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