Construction of Solutions of the Classical Field Equation of a Massless Klein-Gordon Field Interacting with a Static Source

Abstract

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