The Boltzmann Equation in Scalar Field Theory

TL;DR

This paper derives a classical transport equation from quantum scalar field theory, providing a simple iterative expression for the effective action and explicit solutions in the high-temperature static case.

Contribution

It introduces a novel derivation of the classical transport equation directly from quantum field equations in scalar theories, with a new iterative form for the effective action.

Findings

Derived the classical transport equation from quantum scalar field equations.

Provided a simple iterative expression for the effective action.

Presented explicit closed-form solutions in the static, high-temperature limit.

Abstract

We derive the classical transport equation, in scalar field theory with a V(phi) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action which generates all the n-point Green functions in the high-temperature limit. An explicit closed form is given in the static case.