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Quantization of Gravity: Yet Another Way

I. V. Kanatchikov
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Abstract

Recently proposed quantization in field theory based on an analogue of Hamiltonian formulation which treats space and time on equal footing (the so-called De Donder-Weyl theory) is applied to General Relativity in metric variables. We formulate a covariant analogue of the Schroedinger equation for the wave function of space-time and metric variables and a supplementary ``bootstrap condition'' which enables us to incorporate classical metric geometry as an approximate notion - a result of quantum averaging - in the self-consistent with the underlying quantum dynamics way. In this sense an independence of an arbitrarily chosen metric background is ensured.

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I. V. Kanatchikov. 1999-12-22. Quantization of Gravity: Yet Another Way. https://arxiv.org/abs/gr-qc/9912094

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