Generalized definition of time delay in scattering theory

TL;DR

This paper proposes a symmetrized definition of time delay in scattering theory, demonstrating its existence for symmetric regions, its invariance under time reversal, and its relation to classical scattering.

Contribution

It introduces a systematic symmetrized time delay concept applicable to arbitrary symmetric regions, extending previous definitions and analyzing its properties.

Findings

Symmetrized time delay exists for symmetric regions in two-body scattering.

It equals the usual time delay plus a vanishing contribution for spherical regions.

Symmetrized time delay is invariant under time reversal mapping.

Abstract

We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.