3-Dimensional Quantum Gravity  

Based on General Relativity > s.a. quantum gravity; regge calculus and dynamical triangulations.
* Remark: Different, classically equivalent actions may not be equivalent here.
@ Reviews: Carlip LRR(05)gq/04 [spatially closed].
@ 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-in [Chern-Simons and other approaches]; Carlip & Nelson PRD(95)gq/94 [comparison]; Álvarez IJMPD(93)ht/92; Seriu PRD(97)gq/96 [partition function]; Carlip 98; Schroers m.QA/00 [euclidean].
@ With negative cosmological constant: Moncrief & Nelson IJMPD(97)gq [constants of motion]; Yin a0710 [duality to extremal conformal field theory]; Maloney & Witten a0712 [partition function].
@ 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-in.
@ 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 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 ht/05-in, PRL(06) [effective non-commutative quantum field theory]; Oriti & Ryan CQG(06)gq [group field theory approach].
@ 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.
@ 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]; Krasnov CQG(02)gq/01, CQG(02)ht/01, CQG(02)ht [ < 0, black hole creation etc]; Bonzom & Livine a0801 [Immirzi-like parameter]; > s.a. ads-cft; non-commutative gravity; 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).
@ Lorentzian: Gamboa & Mendez NPB(01) [strong coupling, t = 4V]; Ambjørn et al NPPS(02)hl [dynamically triangulated].

Canonical, Metric Representation > s.a. approaches to quantum gravity, including path integrals.
* Possible state: If is the mean curvature of a hypersurface ,

[geometry]:= N exp{–L–1 Sigma  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-in [T2]; Hájícek JMP(98)gq/97 [T2, group-theoretic]; Louko & Matschull CQG(01)gq [2 particles]; Nelson gq/04-in [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: 't Hooft CQG(93)gq [point particles]; Iwasaki JMP(95)gq [Ponzano-Regge]; 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).
@ Loop representation: Husain PRD(91) [general-relativity-like theory]; Nayak GRG(91); Anderson PRD(93)gq/92; Marolf CQG(93)gq, gq/93-in; Carlip gq/93; Ashtekar & Loll CQG(94); Carlip & Nelson PLB(94)gq/93, PRD(99)gq/98; Loll JMP(95)gq [spatially closed]; Ezawa NPB(96)gq/95 [solutions of Hamiltonian constraint]; García-Islas CQG(04)gq/03 [spin networks].
@ Geometrical operators: Livine & Rovelli gq/01-wd [length and time] → Freidel et al CQG(03)gq/02 [length and area].
@ Spin foam: Rovelli PRD(93)ht [Ponzano-Regge-Turaev-Viro-Ooguri]; Zapata JMP(02)gq [continuum]; Oriti & Tlas PRD(06)gq [matter and causality]; Fairbairn & Livine CQG(07)gq [and matter, effective field theory]; Speziale a0706 [coupled to Yang-Mills]; Martins & Mikovic a0804 [perturbation theory].
@ Spin foams, graviton propagator: Speziale JHEP(06)gq/05; Livine et al PRD(07)gq/06; Bonzom et al 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 [quantum holonomies], gq/04-in [quantum holonomies]; Noui & Pérez CQG(05), Noui JMP(06)gq [with pt particles].

Specific Topics and Types of Metrics > s.a. approaches to quantum gravity [pilot wave].
@ Black holes: Bytsenko et al PRD(98) [entropy corrections]; Vaz et al PRD(07) [collapse and radiation, < 0].
@ Other types of metrics: Christodoulakis et al a0806 [axisymmetric, with cosmological constant].
@ Singularities: Kenmoku et al IJMPD(03)gq/02 [conical]; Minassian CQG(02) [BTZ and T2 topology].

Other Theories > s.a. 3D gravity; BRST; quantum gauge theory.
@ Topologically massive gravity: Deser & Yang CQG(90) [1-loop renormalizability].
@ Topological gravity: Bi & Gegenberg CQG(94)gq/93 [loop variables].
@ Related topics: Noui CQG(07)gq/06 [Riemannian, model].

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