On effects of non-Euclidean geometry in quantum theory

TL;DR

This paper develops a quantum scattering theory for particles interacting with cosmic strings, revealing unique effects of string tension on scattering behavior that differ from classical predictions.

Contribution

It introduces a quantum scattering framework for cosmic strings with tension, highlighting how tension influences scattering cross sections in ways not seen in classical models.

Findings

High-frequency scattering cross section differs from classical predictions when string tension is nonzero.

Quantum effects modify scattering behavior, emphasizing the role of string tension.

The S-matrix depends explicitly on flux and tension parameters.

Abstract

Theory of scattering of a quantum-mechanical particle on a cosmic string is developed. S-matrix and scattering amplitude are determined as functions of the flux and the tension of the string. We reveal that, in the case of the nonvanishing tension, the high-frequency limit of the differential scattering cross section does not coincide with the differential cross section for scattering of a classical pointlike particle on a string.