Asymptotic Dynamics in Quantum Field Theory

TL;DR

This paper explores the asymptotic behavior of quantum field theories, especially those with interactions, providing a framework that aligns with perturbation theory and clarifies long-time dynamics.

Contribution

It introduces a new description of asymptotic dynamics in quantum field theories that accounts for weak convergence and physical boundary conditions.

Findings

Consistent with perturbation theory results

Applicable to theories with three and four point interactions

Provides a better understanding of long-time asymptotic behavior

Abstract

A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynamics in field theories which incorporates the important features of weak convergence and physical boundary conditions. Applications to theories with three and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory.