QF1 - Quantum Spacetime |
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Speaker |
Kanatchikov, Igor |
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Coauthors |
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| Talk Title |
Quantum geometry without quantum space-time? |
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Abstract |
The approach to quantization of General Relativity, which is based on the De Donder-Weyl (DW) Hamiltonian formulation rather than the canonical Hamiltonian formalism (a relation and differences between both will be briefly discussed) leads to the description of quantum geometry in terms of the Clifford algebra valued transition amplitudes between different values of spin-connections at difference points of space-time. We derive the covariant Schroedinger equation for those amplitudes. Surprisingly, all the physical constants (G,h,c, \Lambda and the constant of "elementary volume" introduced when the classical differential forms are quantized according to the Poisson-Gerstenhaber brackets of the above mentioned DW formalism) are absorbed in the single dimensionless parameter, which depends on the ordering of operators in the expression of the DW Hamiltonian operator. Thus, when the effective cosmological constant is set to be zero, there is no Planck constant in the remaining part of the covariant Schroedinger equation for quantum general relativity, that points to the purely mathematical meaning of the quantum geometry it describes. We discuss a possible interpretation of the result in terms of the parallel transport of Clifford valued wave functions on the spin-connection bundle. References: [1] I.V. Kanatchikov, Precanonical Quantization and the Schroedinger Wave Functional Revisited, Adv. Theor. Math. Phys. 18 (2014) 1249-1265. [2] I.V. Kanatchikov, On precanonical quantization of gravity, arXiv:1407.3101 |
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