3-Dimensional Quantum Gravity  

Based on General Relativity > s.a. 3D general relativity; quantum gravity; regge calculus and dynamical triangulations.
* Remark: There are various different, but 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].
@ 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.
@ With 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].
@ 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.

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} .

@ References: Hosoya & Nakao PTP(90); Visser PRD(90); Weitsman CMP(91); Carlip CQG(94)gq/93 [Wheeler-DeWitt equation]; Waelbroeck PRD(94); Criscuolo et al gq/95-proc [T2]; Hájíček JMP(98)gq/97 [T2, group-theoretic]; Louko & Matschull CQG(01)gq [2 particles]; Nelson gq/04-fs [ADM, and large diffeomorphisms].

Connection / Loop Representation > s.a. Goldman Bracket; regge calculus; theta sectors.
* Geometry: Quantizing 't Hooft's polygon approach, one finds that the Hamiltonian is cyclic, so time appears to be quantized; This however has been seen as an artifact of the fact that one quantizes a gauge-fixed theory; In Lorentzian quantum gravity, the spectrum of spacelike intervals is continuous, that of timelike intervals discrete.
@ General references: Husain PRD(91) [general-relativity-like topological field theory]; Anderson PRD(93)gq/92 [metric and holonomy formulations]; 't Hooft CQG(93)gq [point particles]; Matschull CQG(95)gq [review]; Waelbroeck & Zapata CQG(96)gq [comparison]; Thiemann CQG(98)gq/97 [Euclidean]; in Ashtekar in(99) [manifold reconstruction]; Noui & Pérez CQG(05)gq/04 [inner product]; Noui CQG(07); Meusburger & Noui ATMP(10)-a0809 [comparison with combinatorial quantization]; Freidel et al PRD(19)-a1811; Shoshany PRD(19)-a1904 [dual polarization].
@ As a Chern-Simons theory: Barbosa et al JPCS(12)-a1206 [complete loop quantization]; Kim & Porrati JHEP-a1508 [on AdS3].
@ Connection representation, lqg: Loll JMP(95)gq [spatially closed]; Ezawa NPB(96)gq/95 [solutions of Hamiltonian constraint]; García-Islas CQG(04)gq/03 [spin networks]; Pérez & Pranzetti CQG(10)-a1001 [with positive cosmological constant, regularization]; Bonzom & Freidel CQG(11)-a1101 [Hamiltonian constraint]; Pranzetti CQG(11)-a1101 [with Λ > 0, physical state]; Noui et al JHEP(11)-a1105, Noui et al JPCS(12)-a1112 [with Λ > 0]; Ben Achour et al PRD(15)-a1306 [role of the Barbero-Immirzi parameter]; Pranzetti PRD(14)-a1402 [and spin-foam quantization]; Girelli & Sellaroli PRD(15)-a1506 [Lorentzian, spinor approach]; Dittrich & Geiller NJP(17)-a1604 [representation from extended topological quantum field theories]; Charles PRD(18)-a1709 [simplicity constraints]; Dittrich a1802 [cosmological constant from defect condensation]; Charles GRG(19)-a1808 [simplified, U(1)3 model with scalar field]; > s.a. 3D black holes.
@ With symmetries, lqc: Zhang PRD(14)-a1411 [lqc]; Cianfrani et al a1606 [symmetries]; Bilski & Marcianò a1707 [with a scalar field clock].
@ Loop representation: Nayak GRG(91); Marolf CQG(93)gq, gq/93; Carlip gq/93; Ashtekar & Loll CQG(94)gq [loop transform]; Carlip & Nelson PLB(94)gq/93, PRD(99)gq/98.
@ Geometrical operators: Livine & Rovelli gq/01-wd [length and time] → Freidel et al CQG(03)gq/02 [length and area]; Ben Achour et al PRD(14)-a1306 [comparison between two formulations]; Ariwahjoedi et al IJGMP(15)-a1503 [curvatures and discrete Gauss-Codazzi equation]; > s.a. discrete spacetime models; geometry of canonical quantum gravity.
@ With matter: Noui & Pérez CQG(05), Noui JMP(06)gq, Freidel et al PRD(19)-a1811 [point particles]; Constantinidis et a CQG(15)-a1403 [AdS gravity and topological matter].
@ Ponzano-Regge state-sum model: Rovelli PRD(93)ht; Iwasaki JMP(95)gq; Livine AHP(16)-a1610 [coarse-graining and q-deformation].
@ Spin foam: Zapata JMP(02)gq [continuum]; Oriti & Tlas PRD(06)gq [matter and causality]; Fairbairn & Livine CQG(07)gq [and matter, effective field theory]; Speziale CQG(07)-a0706 [coupled to Yang-Mills]; Martins & Miković CMP(09)-a0804 [perturbation theory]; Caravelli & Modesto a0905 [spectral dimension]; Xu & Ma PRD(09)-a0908 [emergence of massless Klein-Gordon field].
@ Spin foams, graviton propagator: Speziale JHEP(06)gq/05; Livine et al PRD(07)gq/06; Bonzom et al NPB(08)-a0802.
@ Related topics: Peldán CQG(96)gq/95 [modular-invariant theory]; Marolf et al JMP(97)gq [Euclidean, Diff superselection]; Nelson & Picken PLB(00)gq/99, gq/04-MGX [quantum holonomies]; Delcamp et al a1803 [dual loop quantization]; Dittrich et al CQG(18) [quasi-local holographic dualities].

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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