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].

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