Construction of solutions of the classical field equation for a massless Klein-Gordon field coupled to a static source

TL;DR

This paper constructs solutions to the classical field equation for a massless Klein-Gordon field coupled to a static source, using operator methods in quantum field theory under infrared regularity conditions.

Contribution

It provides a novel method to explicitly construct solutions of the classical field equation from quantum field operators with specific regularity assumptions.

Findings

Sesquilinear form solves the classical field equation

Construction relies on infrared regularity conditions

Operator approach links quantum and classical solutions

Abstract

In this paper, we consider a system of a massless Klein-Gordon field coupled to a static source. The total Hamiltonian is a self-adjoint operator on a boson Fock space. We consider annihilation operators in the Heisenberg picture and define a sesquilinear form. Under infrared regularity conditions, it is proven that the sesquilinear form is a solution of the classical field equation.