Precanonical Quantum Gravity: quantization without the space-time decomposition

Details Precanonical Quantum Gravity: quantization without the space-time decomposition Precanonical Quantum Gravity: quantization without the space-time decomposition

2000-12-20

arxiv.org/abs/gr-qc/0012074v2

Int.J.Theor.Phys. 40 (2001) 1121-1149

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pp, LaTeX, to appear in Int. J. Theor. Phys. v2: LaTeX format of the reference list changed, minor typos fixed

Scientific paper

A nonpertubative approach to quantum gravity using precanonical field quantization originating from the covariant De Donder-Weyl Hamiltonian formulation which treats space and time variables on equal footing is presented. A generally covariant ``multi-temporal'' generalized Schroedinger equation on the finite dimensional space of metric and space-time variables is obtained. An important ingredient of the formulation is the ``bootstrap condition'' which introduces a classical space-time geometry as an approximate concept emerging as the quantum average in a self-consistent with the underlying quantum dynamics manner. An independence of the theory from an arbitrarily fixed background is ensured in this way. The prospects and unsolved problems of precanonical quantization of gravity are outlined.

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