Igor Kanatchikov

Quantum gravity and quantum cosmology from precanonical approach to quantization

Precanonical quantization based on the mathematical structures of the De Donder-Weyl (polysimplectic) covariant Hamiltonian formalism can be applied to general relativity and leads to a new nonperturbative, background independent and covariant formulation of quantum gravity and quantum geometry described in term of the wave functions or transition amplitudes on the bundle of connections over space-time. We formulate the analogue of the Schroedinger equation in this approach and discuss some of its consequences in simple cases, including a simplified quantum cosmology model. Refs: see the forthcoming papers in Arxiv.

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