Abelian 2+1D loop quantum gravity coupled to a scalar field

Witten, E.: (2+1)-Dimensional gravity as an exactly soluble system. Nucl. Phys. B 311, 46 (1988) Freidel, L., Livine, E.R., Rovelli, C.: Spectra of length and area in (2+1) Lorentzian loop quantum gravity. Class. Quant. Gravit. 20, 1463–1478 (2003). arXiv:gr-qc/0212077 Noui, K., Perez, A.: Three-dimensional loop quantum gravity: physical scalar product and spin foam models. Class. Quant. Gravit. 22, 1739–1762 (2005). arXiv:gr-qc/0402110 Date, G., Hossain, G.M.: Matter in loop quantum gravity. SIGMA 8, 010 (2012). arXiv:1110.3874 Giesel, K., Thiemann, T.: Scalar material reference systems and loop quantum gravity. Class. Quant. Gravit. 32, 135015 (2015). arXiv:1206.3807 Bilski, J., Marcianò, A.: 2+1 homogeneous loop quantum gravity with a scalar field clock, arXiv:1707.00723 Thiemann, T.: Kinematical Hilbert spaces for Fermionic and Higgs quantum field theories. Class. Quant. Gravit. 15, 1487–1512 (1998). arXiv:gr-qc/9705021 Ashtekar, A., Lewandowski, J., Sahlmann, H.: Polymer and Fock representations for a scalar field. Class. Quant. Gravit. 20, L11–1 (2003). arXiv:gr-qc/0211012 Kaminski, W., Lewandowski, J., Bobienski, M.: Background independent quantizations: the scalar field. I. Class. Quant. Gravit. 23, 2761–2770 (2006). arXiv:gr-qc/0508091 Kaminski, W., Lewandowski, J., Okolow, A.: Background independent quantizations: the scalar field II. Class. Quant. Gravit. 23, 5547–5586 (2006). arXiv:gr-qc/0604112 Dittrich, B.: Partial and complete observables for Hamiltonian constrained systems. Gen. Relativ. Gravit. 39, 1891–1927 (2007). arXiv:gr-qc/0411013 Thiemann, T.: Anomaly—free formulation of nonperturbative, four-dimensional Lorentzian quantum gravity. Phys. Lett. B 380, 257–264 (1996). arXiv:gr-qc/9606088 Livine, E.R., Tambornino, J.: Holonomy operator and quantization ambiguities on spinor space. Phys. Rev. D 87(10), 104014 (2013). arXiv:1302.7142 Freidel, L., Livine, E.R.: Ponzano–Regge model revisited III: Feynman diagrams and effective field theory. Class. Quant. Gravit. 23, 2021–2062 (2006). arXiv:hep-th/0502106 Freidel, L., Livine, E.R.: Effective 3-D quantum gravity and non-commutative quantum field theory. Phys. Rev. Lett. 96, 221301 (2006). arXiv:hep-th/0512113 Ashtekar, A., Corichi, A., Zapata, J.A.: Quantum theory of geometry III: noncommutativity of Riemannian structures. Class. Quant. Gravit. 15, 2955–2972 (1998). arXiv:gr-qc/9806041 Szabo, R.J.: Quantum field theory on noncommutative spaces. Phys. Rep. 378, 207–299 (2003). arXiv:hep-th/0109162 Smolin, L.: The G(Newton) –> 0 limit of Euclidean quantum gravity. Class. Quant. Gravit. 9, 883–894 (1992). arXiv:hep-th/9202076 Dittrich, B., Geiller, M.: A new vacuum for loop quantum gravity. Class. Quant. Gravit. 32(11), 112001 (2015). arXiv:1401.6441 Bahr, B., Dittrich, B., Geiller, M.: A new realization of quantum geometry, arXiv:1506.08571 Koslowski, T.A.: Dynamical Quantum Geometry (DQG Programme), arXiv:0709.3465 Sahlmann, H.: On loop quantum gravity kinematics with non-degenerate spatial background. Class. Quant. Gravit. 27, 225007 (2010). arXiv:1006.0388 Koslowski, T., Sahlmann, H.: Loop quantum gravity vacuum with nondegenerate geometry. SIGMA 8, 026 (2012). arXiv:1109.4688 Hooft, G.’t: Causality in (2+1)-dimensional gravity. Class. Quant. Gravit. 9, 1335–1348 (1992) Kuchar, K.: Parametrized scalar field on R \(\times \) S(1): dynamical pictures, space-time diffeomorphisms, and conformal isometries. Phys. Rev. D 39, 1579–1593 (1989) Kuchar, K.: Dirac constraint quantization of a parametrized field theory by anomaly—free operator representations of space–time diffeomorphisms. Phys. Rev. D 39, 2263–2280 (1989) Varadarajan, M.: Dirac quantization of parametrized field theory. Phys. Rev. D 75, 044018 (2007). arXiv:gr-qc/0607068 Charles, C.: Simplicity constraints: a 3D toy model for loop quantum gravity. Phys. Rev. D 97(10), 106002 (2018). arXiv:1709.08989 Ashtekar, A., Lewandowski, J.: Quantum theory of geometry. 1: area operators. Class. Quant. Gravit. 14, A55–A82 (1997). arXiv:gr-qc/9602046 Ashtekar, A., Lewandowski, J.: Quantum theory of geometry. 2. Volume operators. Adv. Theor. Math. Phys. 1, 388–429 (1998). arXiv:gr-qc/9711031 Lewandowski, J., Okolow, A., Sahlmann, H., Thiemann, T.: Uniqueness of diffeomorphism invariant states on holonomy-flux algebras. Commun. Math. Phys. 267, 703–733 (2006). arXiv:gr-qc/0504147 Mukhanov, V., Winitzki, S.: Introduction to Quantum Effects in Gravity. Cambridge University Press, Cambridge (2007) Dittrich, B., Geiller, M.: Flux formulation of loop quantum gravity: classical framework. Class. Quant. Gravit. 32(13), 135016 (2015). arXiv:1412.3752 Chamseddine, A.H., Connes, A.: The spectral action principle. Commun. Math. Phys. 186, 731–750 (1997). arXiv:hep-th/9606001