Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time

Version 1 : Received: 7 November 2019 / Approved: 8 November 2019 / Online: 8 November 2019 (11:04:19 CET)

How to cite: Kanatchikov, I.V. Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time. Preprints 2019, 2019110097 (doi: 10.20944/preprints201911.0097.v1). Kanatchikov, I.V. Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time. Preprints 2019, 2019110097 (doi: 10.20944/preprints201911.0097.v1).

## Abstract

A relationship between the functional Schr\"odinger representation and the precanonical quantization of a nonlinear scalar field theory is extended to arbitrary curved space-times. The canonical functional derivative Schr\"odinger equation is derived from the manifestly covariant precanonical Schr\"odinger equation in a singular limiting case when the ultraviolet parameter $\varkappa$ introduced by precanonical quantization is identified with the invariant delta-function at equal spatial points. In the same limiting case, the Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration. Thus the standard QFT in curved space-time in functional Schr\"odinger representation emerges from the precanonical formulation of quantum fields as a singular limiting case.

## Keywords

quantum field theory in curved space-time; De Donder-Weyl Hamiltonian formalism; precanonical quantization; canonical quantization; functional Schrödinger representation

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