Abstract:
The main principle of affine quantum gravity is the strict positivity of the matrix {ˆgab(x)} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle, and they can be replaced by noncanonical, affine commutation relations. Due to the partial second-class nature of the quantum gravitational constraints, it is advantageous to use the projection operator method, which treats all quantum constraints on an equal footing. Using this method, enforcement of regularized versions of the gravitational constraint operators is formulated quite naturally as a novel and relatively well-defined functional integral involving only the same set of variables that appears in the usual classical formulation. Although perturbatively nonrenormalizable, gravity may possibly be understood nonperturbatively from a hard-core perspective that has proved valuable for specialized models.
Citation:
John R. Klauder, “An affinity for affine quantum gravity”, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Collected papers. Dedicated to Academician Andrei Alekseevich Slavnov on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 272, MAIK Nauka/Interperiodica, Moscow, 2011, 180–187; Proc. Steklov Inst. Math., 272 (2011), 169–176
\Bibitem{Kla11}
\by John~R.~Klauder
\paper An affinity for affine quantum gravity
\inbook Problems of modern theoretical and mathematical physics: Gauge theories and superstrings
\bookinfo Collected papers. Dedicated to Academician Andrei Alekseevich Slavnov on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 272
\pages 180--187
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 272
\pages 169--176
\crossref{https://doi.org/10.1134/S0081543811010159}
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Bergeron H., Czuchry E., Gazeau J.P., Malkiewicz P., “Quantum Mixmaster as a Model of the Primordial Universe”, Universe, 6:1 (2020), 7
Frion E., Almeida C.R., “Affine Quantization of the Brans-Dicke Theory: Smooth Bouncing and the Equivalence Between the Einstein and Jordan Frames”, Phys. Rev. D, 99:2 (2019), 023524
Bergeron H., Czuchry E., Malkiewicz P., “Coherent States Quantization and Affine Symmetry in Quantum Models of Gravitational Singularities”, Coherent States and Their Applications: a Contemporary Panorama, Springer Proceedings in Physics, 205, eds. Antoine J., Bagarello F., Gazeau J., Springer-Verlag Berlin, 2018, 281–309
Bergeron H., Gazeau J.-P., “Variations a La Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane”, Entropy, 20:10 (2018), 787
Gazeau J.P., “Covariant Integral Quantizations and Their Applications to Quantum Cosmology”, Acta Polytech., 56:3 (2016), 173–179
Klauder J.R., “Revisiting Canonical Quantization”, Mod. Phys. Lett. A, 29:21 (2014), 1430020
Bergeron H., Gazeau J.P., “Integral Quantizations with Two Basic Examples”, Ann. Phys., 344 (2014), 43–68
Bergeron H., Dapor A., Gazeau J.P., Malkiewicz P., “Smooth Big Bounce From Affine Quantization”, Phys. Rev. D, 89:8 (2014), 083522
Bergeron H., Curado E.M.F., Gazeau J.P., Rodrigues Ligia M. C. S., “Quantizations From (P)Ovm'S”, 8Th International Symposium on Quantum Theory and Symmetries (Qts8), Journal of Physics Conference Series, 512, IOP Publishing Ltd, 2014, 012032
Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau, Theoretical and Mathematical Physics, Coherent States, Wavelets, and Their Generalizations, 2014, 1
Claus Kiefer, “Conceptual Problems in Quantum Gravity and Quantum Cosmology”, ISRN Mathematical Physics, 2013 (2013), 1
Klauder J.R., “The Utility of Affine Variables and Affine Coherent States”, J. Phys. A-Math. Theor., 45:24, SI (2012), 244001
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