De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Kanatchikov, I.V.^1

National Center of Quantum Information in Gdansk, 81-824 Sopot, Poland^1

关键词: Connection coefficients;    Differential operators;    Dinger equation;    Hamiltonian formulations;    Invariant measure;    Quantum geometry;    Singularity avoidance;    Transition amplitudes;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012041/pdf
DOI  :  10.1088/1742-6596/442/1/012041

学科分类：力学，机械学

来源: IOP

【 摘 要 】

The De Donder-Weyl (DW) covariant Hamiltonian formulation of the Palatini first-order Lagrangian of vielbein (tetrad) gravity and its precanonical quantization are presented. No splitting into 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 Schrodinger 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.