QG1 - Loop Quantum Gravity |
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Speaker |
Kanatchikov, Igor |
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| Talk Title |
Canonical Quantum Gravity as a Limiting Case of Precanonical Quantization |
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Abstract |
We discuss a possible relation between the constructions of canonical quantum gravity in various formulations and the recently proposed precanonical quantization approach to quantum gravity which avoids the procedure of space-time decomposition. We present our results on the relation between precanonical quantization and the functional Schroedinger representation in the case of scalar fields, Yang-Mills fields, and scalar fields in curved space-time in order to argue that the theories resulting from the canonical quantization in the functional Schroedinger representation can be viewed as a singular limiting case corresponding to the infinite value of the ultraviolet parameter $varkappa$ which is introduced in precanonical quantization when a differential form corresponding to an infinitesimal spatial volume is represented by an element of Clifford algebra. References: 1. I.V. Kanatchikov, On the precanonical structure of the Schr\"o\-dinger wave functional, Adv. Theor. Math. Phys. 20 (2016) 1377, arXiv:1312.4518 [hep-th], 2. I. V. Kanatchikov, Schroedinger wave functional in quantum Yang-Mills theory from precanonical quantization, arXiv:1805. to appear, 3. I.V. Kanatchikov, On the ``spin-connection foam" picture of quantum gravity from precanonical quantization, MG14 Proceedings, arXiv:1512.09137 [gr-qc], 4. I.V. Kanatchikov, De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity, arXiv:1302.2610 [gr-qc]. |
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