Non-Gaussian Path Integration in Self-Interacting Scalar Field Theories

TL;DR

This paper introduces a new perturbative approach for self-interacting scalar field theories using non-Gaussian path integrals, revealing the triviality of the theory in the continuum limit under certain conditions.

Contribution

It proposes a novel perturbation scheme combining kinetic expansion with standard perturbation theory for scalar fields.

Findings

Kinetic expansion simplifies the path integral to a product of ordinary integrals.

The new scheme facilitates exact evaluation of non-Gaussian path integrals.

The theory becomes trivial in the continuum limit when parameters are fixed to a non-Gaussian path integral without kinetic term.

Abstract

In self-interacting scalar field theories kinetic expansion is an alternative way of calculating the generating functional for Green's functions where the zeroth order non-Gaussian path integral becomes diagonal in x-space and reduces to the product of an ordinary integral at each point which can be evaluated exactly. We discuss how to deal with such functional integrals and propose a new perturbative expansion scheme which combines the elements of the kinetic expansion with that of usual perturbation theory. It is then shown that, when the cutoff dependent bare parameters in the potential are fixed to have a well defined non-Gaussian path integral without the kinetic term, the theory becomes trivial in the continuum limit.