Asymptotic Analysis of the Ponzano–Regge Model with Non-Commutative Metric Boundary Data
Daniele Oriti, Matti Raasakka

Список литературы
1.	Alexandrov S., Geiller M., Noui K., “Spin foams and canonical quantization”, SIGMA, 8 (2012), 055, 79 pp., arXiv: 1112.1961
2.	Baez J. C., “An introduction to spin foam models of {$BF$} theory and quantum gravity”, Geometry and Quantum Physics ({S}chladming, 1999), Lecture Notes in Phys., 543, Springer, Berlin, 2000, 25–93, arXiv: gr-qc/9905087
3.	Bahr B., Dittrich B., “({B}roken) gauge symmetries and constraints in {R}egge calculus”, Classical Quantum Gravity, 26 (2009), 225011, 34 pp., arXiv: 0905.1670
4.	Baratin A., Dittrich B., Oriti D., Tambornino J., “Non-commutative flux representation for loop quantum gravity”, Classical Quantum Gravity, 28 (2011), 175011, 19 pp., arXiv: 1004.3450
5.	Baratin A., Girelli F., Oriti D., “Diffeomorphisms in group field theories”, Phys. Rev. D, 83 (2011), 104051, 22 pp., arXiv: 1101.0590
6.	Baratin A., Oriti D., “Group field theory with noncommutative metric variables”, Phys. Rev. Lett., 105 (2010), 221302, 4 pp., arXiv: 1002.4723
7.	Baratin A., Oriti D., “Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett–Crane model”, New J. Phys., 13 (2011), 125011, 28 pp., arXiv: 1108.1178
8.	Baratin A., Oriti D., “Group field theory and simplicial gravity path integrals: a model for Holst–Plebański gravity”, Phys. Rev. D, 85 (2012), 044003, 15 pp., arXiv: 1111.5842
9.	Barrett J. W., Crane L., “Relativistic spin networks and quantum gravity”, J. Math. Phys., 39 (1998), 3296–3302, arXiv: gr-qc/9709028
10.	Barrett J. W., Dowdall R. J., Fairbairn W. J., Hellmann F., Pereira R., “Lorentzian spin foam amplitudes: graphical calculus and asymptotics”, Classical Quantum Gravity, 27 (2010), 165009, 34 pp., arXiv: 0907.2440
11.	Barrett J. W., Naish-Guzman I., “The Ponzano–Regge model”, Classical Quantum Gravity, 26 (2011), 155014, 48 pp., arXiv: 0803.3319
12.	Boulatov D. V., “A model of three-dimensional lattice gravity”, Modern Phys. Lett. A, 7 (1992), 1629–1646, arXiv: hep-th/9202074
13.	Caselle M., D'Adda A., Magnea L., “Regge calculus as a local theory of the {P}oincaré group”, Phys. Lett. B, 232 (1989), 457–461
14.	Chaichian M., Demichev A., Path integrals in physics, v. I, Series in Mathematical and Computational Physics, Stochastic processes and quantum mechanics, Institute of Physics Publishing, Bristol, 2001
15.	Conrady F., Freidel L., “Semiclassical limit of 4-dimensional spin foam models”, Phys. Rev. D, 78 (2008), 104023, 18 pp., arXiv: 0809.2280
16.	Dittrich B., Guedes C., Oriti D., “On the space of generalized fluxes for loop quantum gravity”, Classical Quantum Gravity, 30 (2013), 055008, 24 pp., arXiv: 1205.6166
17.	Dowdall R. J., Gomes H., Hellmann F., “Asymptotic analysis of the {P}onzano-{R}egge model for handlebodies”, J. Phys. A: Math. Theor., 43 (2010), 115203, 27 pp., arXiv: 0909.2027
18.	Dupuis M., Girelli F., Livine E., “Spinors and {V}oros star-product for group field theory: first contact”, Phys. Rev. D, 86 (2012), 105034, 18 pp., arXiv: 1107.5693
19.	Dupuis M., Livine E. R., “Holomorphic simplicity constraints for 4{D} spinfoam models”, Classical Quantum Gravity, 28 (2011), 215022, 32 pp., arXiv: 1104.3683
20.	Engle J., Livine E., Pereira R., Rovelli C., “L{QG} vertex with finite {I}mmirzi parameter”, Nuclear Phys. B, 799 (2008), 136–149, arXiv: 0711.0146
21.	Engle J., Pereira R., Rovelli C., “Loop-quantum-gravity vertex amplitude”, Phys. Rev. Lett., 99 (2007), 161301, 4 pp., arXiv: 0705.2388
22.	Freidel L., “Group field theory: an overview”, Internat. J. Theoret. Phys., 44 (2005), 1769–1783, arXiv: hep-th/0505016
23.	Freidel L., Krasnov K., “A new spin foam model for 4{D} gravity”, Classical Quantum Gravity, 25 (2008), 125018, 36 pp., arXiv: 0708.1595
24.	Freidel L., Livine E. R., “3{D} quantum gravity and effective noncommutative quantum field theory”, Phys. Rev. Lett., 96 (2006), 221301, 4 pp., arXiv: hep-th/0512113
25.	Freidel L., Majid S., “Noncommutative harmonic analysis, sampling theory and the {D}uflo map in {$2+1$} quantum gravity”, Classical Quantum Gravity, 25 (2008), 045006, 37 pp., arXiv: hep-th/0601004
26.	Goldman W. M., “The symplectic nature of fundamental groups of surfaces”, Adv. Math., 54 (1984), 200–225
27.	Guedes C., Oriti D., Raasakka M., “Quantization maps, algebra representation, and non-commutative {F}ourier transform for {L}ie groups”, J. Math. Phys., 54 (2013), 083508, 31 pp., arXiv: 1301.7750
28.	Han M., “On spinfoam models in large spin regime”, Classical Quantum Gravity, 31 (2013), 015004, 21 pp., arXiv: 1304.5627
29.	Han M., “Semiclassical analysis of spinfoam model with a small {B}arbero–{I}mmirzi parameter”, Phys. Rev. D, 88 (2013), 044051, 13 pp., arXiv: 1304.5628
30.	Han M., Krajewski T., “Path integral representation of {L}orentzian spinfoam model, asymptotics and simplicial geometries”, Classical Quantum Gravity, 31 (2014), 015009, 34 pp., arXiv: 1304.5626
31.	Han M., Zhang M., “Asymptotics of the spin foam amplitude on simplicial manifold: {E}uclidean theory”, Classical Quantum Gravity, 29 (2012), 165004, 40 pp., arXiv: 1109.0500
32.	Han M., Zhang M., “Asymptotics of spinfoam amplitude on simplicial manifold: {L}orentzian theory”, Classical Quantum Gravity, 30 (2013), 165012, 57 pp., arXiv: 1109.0499
33.	Hellmann F., Kamiński W., Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations, arXiv: 1210.5276
34.	Hellmann F., Kamiński W., “Holonomy spin foam models: asymptotic geometry of the partition function”, J. High Energy Phys., 2013:10 (2013), 165, 63 pp., arXiv: 1307.1679
35.	Joung E., Mourad J., Noui K., “Three dimensional quantum geometry and deformed symmetry”, J. Math. Phys., 50 (2009), 052503, 29 pp., arXiv: 0806.4121
36.	Kamiński W., Steinhaus S., “Coherent states, {$6j$} symbols and properties of the next to leading order asymptotic expansions”, J. Math. Phys., 54 (2013), 121703, 58 pp., arXiv: 1307.5432
37.	Kawamoto N., Nielsen H. B., “Lattice gauge gravity”, Phys. Rev. D, 43 (1991), 1150–1156
38.	Magliaro E., Perini C., “Regge gravity from spinfoams”, Internat. J. Modern Phys. D, 22 (2013), 1350001, 21 pp., arXiv: 1105.0216
39.	Majid S., Schroers B. J., “{$q$}-deformation and semidualization in 3{D} quantum gravity”, J. Phys. A: Math. Gen., 42 (2009), 425402, 40 pp., arXiv: 0806.2587
40.	Mizoguchi S., Tada T., “Three-dimensional gravity from the {T}uraev–{V}iro invariant”, Phys. Rev. Lett., 68 (1992), 1795–1798, arXiv: hep-th/9110057
41.	Noui K., Perez A., “Three-dimensional loop quantum gravity: physical scalar product and spin-foam models”, Classical Quantum Gravity, 22 (2005), 1739–1761, arXiv: gr-qc/0402110
42.	Noui K., Perez A., Pranzetti D., “Canonical quantization of non-commutative holonomies in {$2+1$} loop quantum gravity”, J. High Energy Phys., 2011:10 (2011), 036, 21 pp., arXiv: 1105.0439
43.	Noui K., Perez A., Pranzetti D., “Non-commutative holonomies in $2+1$ LQG and Kauffman's brackets”, J. Phys. Conf. Ser., 360 (2012), 012040, 4 pp., arXiv: 1112.1825
44.	Oriti D., “The microscopic dynamics of quantum space as a group field theory”, Foundations of Space and Time: Reflections on Quantum Gravity, eds. J. Murugan, A. Weltman, G. Ellis, Cambridge University Press, Cambridge, 2012, 257–320, arXiv: 1110.5606
45.	Oriti D., Raasakka M., “Quantum mechanics on {${\rm SO}(3)$} via non-commutative dual variables”, Phys. Rev. D, 84 (2011), 025003, 18 pp., arXiv: 1103.2098
46.	Perelomov A., Generalized coherent states and their applications, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1986
47.	Perez A., “The new spin foam models and quantum gravity”, Papers Phys., 4 (2012), 040004, 37 pp., arXiv: 1205.0911
48.	Perez A., “The spin foam approach to quantum gravity”, Living Rev. Relativ., 16 (2013), 3, 128 pp., arXiv: 1205.2019
49.	Ponzano G., Regge T., “Semiclassical limit of Racah coefficients”, Spectroscopy and Group Theoretical Methods in Physics, ed. F. Block, North Holland, Amsterdam, 1968, 1–58
50.	Pranzetti D., “Turaev–Viro amplitudes from $2+1$ loop quantum gravity”, Phys. Rev. D, 89 (2014), 084058, 14 pp., arXiv: 1402.2384
51.	Regge T., Williams R. M., “Discrete structures in gravity,”, J. Math. Phys., 41 (2000), 3964–3984, arXiv: gr-qc/0012035
52.	Reisenberger M. P., Rovelli C., ““{S}um over surfaces” form of loop quantum gravity”, Phys. Rev. D, 56 (1997), 3490–3508, arXiv: gr-qc/9612035
53.	Reshetikhin N., Turaev V. G., “Invariants of {$3$}-manifolds via link polynomials and quantum groups”, Invent. Math., 103 (1991), 547–597
54.	Rovelli C., “Basis of the {P}onzano–{R}egge–{T}uraev–{V}iro–{O}oguri quantum-gravity model is the loop representation basis”, Phys. Rev. D, 48 (1993), 2702–2707, arXiv: hep-th/9304164
55.	Rovelli C., Quantum gravity, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 2004
56.	Sahlmann H., Thiemann T., “Chern–{S}imons theory, {S}tokes' theorem, and the {D}uflo map”, J. Geom. Phys., 61 (2011), 1104–1121, arXiv: 1101.1690
57.	Sahlmann H., Thiemann T., “Chern–Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map”, Phys. Rev. Lett., 108 (2012), 111303, 5 pp., arXiv: 1109.5793
58.	Schroers B. J., “Combinatorial quantization of {E}uclidean gravity in three dimensions”, Quantization of Singular Symplectic Quotients, Progr. Math., 198, eds. N. Landsman, M. Pflaum, M. Schlichenmaier, Birkhäuser, Basel, 2001, 307–327, arXiv: math.QA/0006228
59.	Sengupta A. N., “The volume measure for flat connections as limit of the {Y}ang–{M}ills measure”, J. Geom. Phys., 47 (2003), 398–426
60.	Thiemann T., Modern canonical quantum general relativity, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 2007
61.	Turaev V. G., Viro O. Y., “State sum invariants of {$3$}-manifolds and quantum {$6j$}-symbols”, Topology, 31 (1992), 865–902
62.	Witten E., “Quantum field theory and the {J}ones polynomial”, Comm. Math. Phys., 121 (1989), 351–399
63.	Witten E., “On quantum gauge theories in two dimensions”, Comm. Math. Phys., 141 (1991), 153–209