Towards a "pre-canonical" quantization of gravity without the space+time decomposition

Details Towards a "pre-canonical" quantization of gravity without the space+time decomposition Towards a "pre-canonical" quantization of gravity without the space+time decomposition

1999-09-09

arxiv.org/abs/gr-qc/9909032v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, LaTeX2e

Scientific paper

Quantization of gravity is discussed in the context of field quantization based on an analogue of canonical formalism (the De Donder-Weyl canonical theory) which does not require the space+time decomposition. Using Horava's (1991) De Donder-Weyl formulation of General Relativity we put forward a covariant generalization of the Schr\"odinger equation for the wave function of space-time and metric variables and a supplementary ``bootstrap condition'' which self-consistently incorporates the classical background space-time geometry as a quantum average and closes the system of equations. Some open questions for further research are outlined.

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