3-Dimensional Quantum Gravity – Connection Representation| 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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