A Version of Exclusively Perturbative Quantum Field Theory

TL;DR

This paper proposes a reformulation of renormalizable Quantum Field Theory that eliminates non-perturbative effects by applying specific boundary conditions to all fields in the functional integral, making the theory purely perturbative.

Contribution

It introduces a version of Quantum Field Theory where non-perturbative effects are absent by using boundary conditions consistently across all fields in the generating functional.

Findings

Non-perturbative effects are eliminated in the proposed formulation.

The generating functional can be expressed as a unique, exact compact formula.

Perturbation theory fully determines the generating functional.

Abstract

We suggest a version of renormalizable Quantum Field Theory which does not contain non-perturbative effects. This is otained by the proper use of the boundary conditions in the functional integral of the generating functional of Green functions. It is well known which boundary conditions are applied to the fields of the functional integral to get correct perturbation theory. We propose that these conditions should be used for all fields integrated in the generating functional integral. It is shown that in this case non-perturbative effects are absent. That is we assume that perturbation theory defines the complete generating functional integral. It allows, in particular, to formulate the generating functional integral in a unique way as an exact compact mathematical formula.