3-Dimensional Quantum Gravity – Connection Representation  

In General > 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: Anderson PRD(93)gq/92 [metric and holonomy formulations]; 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 [particle-like edge modes]; Shoshany PRD(19)-a1904 [dual polarization].
@ Loop quantum gravity: 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].
@ 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.

Spin-Foam Models
@ 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]; Goeller et al GRG(20) [boundary states and exact partition function].
@ 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].

Other Approaches and Variations
@ With point particles: 't Hooft CQG(93)gq; Noui & Pérez CQG(05); Noui JMP(06)gq; Freidel et al PRD(19)-a1811.
@ Other matter: Constantinidis et a CQG(15)-a1403 [AdS gravity and topological matter].
@ As a Chern-Simons theory: Barbosa et al JPCS(12)-a1206 [complete loop quantization]; Kim & Porrati JHEP-a1508 [on AdS3].
@ 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.
@ Ponzano-Regge state-sum model: Rovelli PRD(93)ht; Iwasaki JMP(95)gq; Livine AHP(16)-a1610 [coarse-graining and q-deformation].
@ Topological gravity: Husain PRD(91) [general-relativity-like topological field theory]; > s.a. 3D quantum gravity.

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