Precanonical structure of the Schr\"odinger wave functional in curved space-time

TL;DR

This paper extends the relationship between the functional Schr"odinger representation and precanonical quantization of scalar fields to curved space-time, showing how standard QFT emerges as a limit of precanonical formulation.

Contribution

It derives the Schr"odinger functional equation from a covariant precanonical Schr"odinger equation in curved space-time and expresses the wave functional as a trace of Clifford-algebra-valued functions.

Findings

Standard QFT in Schr"odinger form emerges as a limit of precanonical quantization.

The functional Schr"odinger equation is derived from a covariant precanonical framework.

Wave functional expressed as a trace of Clifford-algebra-valued functions.

Abstract

A relationship between the functional Schr\"odinger representation and the precanonical quantization of a scalar field theory is extended to an arbitrary curved space-time. The canonical functional derivative Schr\"odinger equation is derived from the manifestly covariant precanonical Schr\"odinger equation and the Schr\"odinger 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 Schr\"odinger representation emerges from the precanonical formulation of quantum fields as a singular limiting case.