Precanonical structure of the Schrödinger wave functional in curved space-time

Abstract

A relationship between the functional Schrödinger representation and the precanonical quantization of a scalar field theory is extended to an arbitrary curved space-time. The canonical functional derivative Schrödinger equation is derived from the manifestly covariant precanonical Schrödinger equation and the Schrödinger wave functional is expressed as the trace of the product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration when the ultraviolet parameter $\varkappa$ introduced in precanonical quantization is infinite. Thus the standard QFT in functional Schrödinger representation emerges from the precanonical formulation of quantum fields as a singular limiting case.

13 pages. arXiv admin note: text overlap with arXiv:1810.09968

References in corpus (4)

• On precanonical quantization of gravity
• Covariant Hamiltonian formalism for the calculus of variations with several variables
• Ehrenfest Theorem in Precanonical Quantization
• On the relation between the canonical Hamilton-Jacobi equation and the De Donder-Weyl Hamilton-Jacobi formulation in general relativity

Cited by in corpus (1)

• On the relation between the canonical Hamilton-Jacobi equation and the De Donder-Weyl Hamilton-Jacobi formulation in general relativity