3-Dimensional Quantum Gravity| 3-Dimensional Quantum Gravity |
Based on General Relativity
> s.a. 3D general relativity; connection representation;
quantum gravity; regge calculus and dynamical
triangulations.
* Remark: There are various different,
classically equivalent actions, which may lead to inequivalent quantum theories.
@ Books, reviews: Carlip 98;
Carlip LRR(05)gq/04 [spatially closed];
Carlip SA(12)apr.
@ General references: Martinec PRD(84);
Witten NPB(88);
Nelson & Regge NPB(89),
CMP(91),
PLB(91),
PRD(94)gq/93;
Carlip PRD(92),
gq/93-conf [Chern-Simons and other approaches];
Carlip & Nelson PRD(95)gq/94 [comparison];
Álvarez IJMPD(93)ht/92;
Seriu PRD(97)gq/96 [partition function];
Schroers m.QA/00 [euclidean];
Basu a0902-wd [spatial topology];
Catterall PoS-a1010
[on a lattice, and twisted supersymmetric Yang-Mills theory];
Hamber et al PRD(12)-a1207 [on a lattice, infrared structure];
Chen et al CQG(14) [on non-orientable manifolds];
Canepa & Schiavina a1905 [BV-BFV description].
@ With negative cosmological constant: Moncrief & Nelson IJMPD(97)gq [constants of motion];
Krasnov CQG(02)gq/01,
CQG(02)ht/01,
CQG(02)ht [black-hole creation etc];
Yin a0710 [duality to extremal conformal field theory];
Maloney & Witten JHEP(10)-a0712 [partition function, contribution from classical geometries];
Kraus et al a2103
[in a box, Dirichlet boundary conditions].
@ BRST approach:
González & Pullin PRD(90);
Fülöp MPLA(92)gq.
@ Observables: Carlip PRD(90) [in ADM and ISO(2,1) approaches];
Nelson & Regge CMP(93);
Nelson GRG(95)gq;
Carbone et al CQG(02)gq/01,
Pierri gq/02 [volume operator];
Barrett IJMPA(03)gq/02-conf.
@ Lorentzian: Ambjørn et al APPB(03)ht [asymmetric ABAB matrix model].
@ Renormalizability / finiteness: Anselmi NPB(04)ht/03,
NPB(04)ht/03 [coupled to conformal field theory];
> s.a. renormalization.
@ With Barbero-Immirzi-like parameter: Bonzom & Livine CQG(08)-a0801;
Basu & Paul CQG(10)-a0909 [2-torus spatial sections];
Barbosa et al CQG(12)-a1204 [partial gauge fixing and reduction to an SU(2) Chern-Simons theory].
@ Related topics:
Carlip PRD(93) [and operator ordering];
Soleng PS(93) [as vacuum polarization];
Barrett & Crane CQG(97)gq/96 [and topological state sums];
Ambjørn et al JHEP(01)ht [and matrix model];
> s.a. ads-cft; non-commutative gravity;
Tensor Models; topology change
and models.
With Matter
@ Coupled to point particles: Kabat & Ortiz PRD(94)ht/93;
Matschull & Welling CQG(98)gq/97;
Cantini & Menotti CQG(03) [functional approach];
Krasnov CQG(07)ht/05 [group field theory approach].
@ With matter fields:
Carlip & Gegenberg PRD(91) [topological matter];
Pierri IJMPD(02)gq/01 [scalar, from Gowdy reduction];
Barrett CQG(06)gq/05 [quantum field theory + quantum gravity];
Freidel et al gq/05 [scalar];
Freidel & Livine PRL(06)ht/05-proc [effective non-commutative quantum field theory];
Oriti & Ryan CQG(06)gq [group field theory approach];
Husain & Ziprick PRD(15)-a1506 [with dust].
Path Integral > s.a. boundary conditions
in quantum cosmology [Hartle-Hawking]; regge calculus.
@ Euclidean:
Carlip CQG(93) [sum over topologies],
CQG(95)gq;
Guadagnini & Tomassini PLB(94);
Castro et al PRD(11)-a1103
[including perturbative loop corrections and non-perturbative instanton corrections];
Iizuka et al PRL(15)-a1504,
Honda et al PRD(16)-a1510 [with Λ < 0].
@ Lorentzian: Gamboa & Mendez NPB(01)ht/00
[strong coupling, t = 4V];
Ambjørn et al NPPS(02)hl [dynamically triangulated];
Arias & Schaposnik IJMPA(11)-a1101 [self-dual].
Canonical, Metric Representation
> s.a. approaches to quantum gravity, including path integrals.
* Possible state: If
κ is the mean curvature of a hypersurface Σ,
Ψ[geometry]:= N exp{−L−1 ∫Σ κ d2v} .
@ General references:
Hosoya & Nakao PTP(90);
Visser PRD(90);
Weitsman CMP(91);
Carlip CQG(94)gq/93 [Wheeler-DeWitt equation];
Waelbroeck PRD(94);
Louko & Matschull CQG(01)gq [2 particles];
Nelson gq/04-fs [ADM, and large diffeomorphisms].
@ 2-torus topology:
Criscuolo et al gq/95-proc;
Hájíček JMP(98)gq/97 [group-theoretic];
Specific Topics and Types of Metrics
> s.a. approaches to quantum gravity [pilot-wave interpretation].
@ Collapse: Ortíz & Ryan JPCS(07)gq,
GRG(07) [dust];
Vaz et al PRD(07)-a0710 [and Hawking radiation];
Sarkar et al PRD(16)-a1602 [dust].
@ Black holes:
Bytsenko et al PRD(98) [entropy corrections];
Vaz et al PRD(07) [collapse and radiation, Λ < 0];
> s.a. 3D black holes.
@ Other types of metrics:
Christodoulakis et al CQG(08)-a0806 [G1, with cosmological constant];
> s.a. bianchi-I quantum cosmology.
@ Singularities: Kenmoku et al IJMPD(03)gq/02 [conical];
Minassian CQG(02)
[BTZ and T2 topology];
Raeymaekers JHEP(15)-a1412 [quantization of conical spaces].
Other Theories > s.a. 3D gravity
and massive gravity; BRST transformations;
higher-order theories; modified approaches;
quantum gauge theory.
@ Topological gravity: Bi & Gegenberg CQG(94)gq/93 [loop variables].
@ Hořava-lifshitz gravity:
Griffin et al JHEP(17)-a1701;
Barvinsky et al PRL(17)-a1706 [asymptotic freedom].
@ Related topics: Noui CQG(07)gq/06 [Riemannian, model].
main page
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