1999/09/09 by I. V. Kanatchikov, Igor V. Kanatchikov, Kanatchikov, I. V.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9909032
19 pages, LaTeX2e
arxiv created 1999/09/09 · openalex publication_date 1999/09/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.