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

I. V. Kanatchikov
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Abstract

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 Schrödinger 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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I. V. Kanatchikov. 1999-09-09. Towards a "pre-canonical" quantization of gravity without the space+time decomposition. https://arxiv.org/abs/gr-qc/9909032

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