An exact integration of a \phi^4 quantum field theory

TL;DR

This paper introduces a novel method to exactly compute the non-perturbative path integral of a 3+1-D scalar  quantum field theory by transforming the exponential integral into a product of Heaviside functions, enabling exact solutions.

Contribution

It presents a new exact integration technique for  quantum field theories using a statistical equivalence to uniform distributions, which was not previously available.

Findings

Exact non-perturbative path integral for 3+1-D  theory calculated.

Demonstrates the statistical equivalence between exponential path integrals and products of Heaviside functions.

Provides a new analytical tool for solving certain quantum field theories.

Abstract

Most quantum field theories are not exactly solvable. In this paper show the statistical equivalence of the standard exponential path integral to products of Heaviside functions, i.e. a product of specially tuned uniform distributions. This allows exact integrations of certain quantum field theories. I apply the equivalence to calculate the exact, non-perturbative path integral for a 3+1-D scalar (real) phi-4 field theory.