Asymptotic Analysis of a Non-Linear Non-Local Integro-Differential Equation Arising from Bosonic Quantum Field Dynamics

TL;DR

This paper studies a family of non-linear, non-local integro-differential equations derived from bosonic quantum field theory, proving existence, uniqueness, and convergence of solutions to a limit equation.

Contribution

It introduces a new family of equations from quantum field theory and establishes their well-posedness and convergence properties.

Findings

Existence and uniqueness of strong global solutions

Uniform convergence of solutions to the limit equation

Framework connecting quantum field derivations to integro-differential equations

Abstract

We introduce a one parameter family of non-linear, non-local integro-differential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of the solutions of the one parameter family towards the solution of the limit equation.