2013/02/28 by I. V. Kanatchikov, I V Kanatchikov · 18 citations
Mathematics · Physics and Astronomy · Social Sciences · #Canonical quantization #Connection (principal bundle) #Covariant transformation #Hamiltonian (control theory) #Hilbert space #Immirzi parameter #International Science and Diplomacy #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Quantum and Classical Electrodynamics #Singularity #Spin connection #gr-qc #hep-th #math-ph #math.MP #quant-ph
paper · pdf · open access · doi:10.1088/1742-6596/442/1/012041
published in Journal of Physics Conference Series 442, 012041 (IOP Publishing) · 14 pages. v2 corrects small typos in (35) and the equation preceding (12)
openalex publication_date 2013/06/10 · arxiv created 2015/01/27 · arxiv updated 2015/01/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The De Donder-Weyl (DW) covariant Hamiltonian formulation of Palatini first-order Lagrangian of vielbein (tetrad) gravity and its precanonical quantization are presented. No splitting into the space and time is required in this formulation. Our recent generalization of Dirac brackets is used to treat the second class primary constraints appearing in the DW Hamiltonian formulation and to find the fundamental brackets. Quantization of the latter yields the representation of vielbeins as differential operators with respect to the spin connection coefficients, and the Dirac-like precanonical Schr"odinger equation on the space of spin connection coefficients and space-time variables. The transition amplitudes on this space describe the quantum geometry of space-time. We also discuss the Hilbert space of the theory, the invariant measure on the spin connection coefficients, and point to the possible quantum singularity avoidance built in in the natural choice of the boundary conditions of the wave functions on the space of spin connection coefficients.