Multimomentum Hamiltonian Formalism in Quantum Field Theory

TL;DR

This paper introduces a rigorous multimomentum Hamiltonian formalism in quantum field theory, defining generating functionals as Fourier transforms of Gaussian measures in nuclear spaces, extending the canonical variables to all spacetime coordinates.

Contribution

It develops a non-perturbative framework for quantum field theory by formulating generating functionals as measures in multimomentum variables, overcoming limitations of traditional perturbative approaches.

Findings

Defines generating functionals as Fourier transforms of Gaussian measures in nuclear spaces.

Extends canonical variables to include derivatives with respect to all spacetime coordinates.

Provides a mathematically rigorous foundation for quantum field theory beyond perturbation theory.

Abstract

The familiar generating functionals in quantum field theory fail to be true measures and, so they make the sense only in the framework of the perturbation theory. In our approach, generating functionals are defined strictly as the Fourier transforms of Gaussian measures in nuclear spaces of multimomentum canonical variables when field momenta correspond to derivatives of fields with respect to all world coordinates, not only to time.