1999/12/22 by I. V. Kanatchikov
Physics and Astronomy · #gr-qc
published as in "Coherent States, Quantization and Gravity," Eds. M. Schlichenmaier, A. Strasburger, S. T. Ali and A. Odzijewicz, Warsaw University Press, Warsaw 2001; pp. 189-197. · 8 pages, LaTeX2e. Based on author's talks at the XV Workshop on Geometrical Methods in Physics (Bialowieza, Poland, 1998) and XXXI Symposium on Mathematical Physics (Torun, Poland, 1999). To appear in Rep. Math. Phys. (2000)
arxiv created 1999/12/22 · arxiv updated 2009/11/30
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.