Precanonical Quantization and the Schroedinger Wave Functional

TL;DR

This paper explores the relationship between the traditional Schrödinger wave functional and a Clifford-valued wave function in precanonical quantization, deriving the standard functional Schrödinger equation from a covariant framework.

Contribution

It introduces a covariant precanonical quantization approach linking Clifford-valued wave functions to the Schrödinger wave functional, providing a new perspective on quantum field theory.

Findings

Derived the standard functional Schrödinger equation from a covariant Dirac-like equation.

Showed the Schrödinger wave functional as a trace over Clifford-valued wave functions.

Established a connection between precanonical quantization and traditional quantum field theory.

Abstract

A relation between the Schroedinger wave functional and the Clifford-valued wave function which appears in what we call precanonical quantization of fields and fulfills a Dirac-like generalized covariant Schroedinger equation on the space of field and space-time variables is discussed. The Schroedinger wave functional is argued to be the trace of the positive frequency part of the continual product over all spatial points of the values of the aforementioned wave function restricted to a Cauchy surface. The standard functional differential Schroedinger equation is derived as a consequence of the Dirac-like covariant Schroedinger equation.