Slowly decaying classical fields, unitarity, and gauge invariance

TL;DR

This paper investigates the challenges of defining a unitary scattering operator in classical gauge fields that decay slowly, highlighting issues with gauge invariance and interpretation in expanding systems.

Contribution

It reveals conditions under which unitarity fails for slowly decaying gauge fields and discusses implications for gauge invariance and system evolution interpretation.

Findings

Unitarity of the S-matrix is not guaranteed for slowly decaying gauge fields.

Gauge invariance issues are intertwined with unitarity problems in these systems.

Expanding systems exemplify the challenges in defining a consistent scattering framework.

Abstract

In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the field goes to zero. The importance of this point is exposed for the counter-example of low-dimensionally expanding systems. The issues of gauge invariance and of the interpretation of the evolution at intermediate times are also intricately linked to that point.