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Precanonical quantum gravity: Quantization without the space-time decomposition. (English) Zbl 0984.83026

Summary: 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 an equal footing, is presented. A generally covariant “multitemporal” generalized Schrödinger 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 self-consistent with the underlying quantum dynamics. This ensures the independence of the theory from an arbitrarily fixed background. The prospects and unsolved problems of precanonical quantization of gravity are outlined.

MSC:

83C45 Quantization of the gravitational field
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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