# Quantum Scattering on a Cone revisited

## TL;DR

This paper analyzes quantum scattering on a conical spacetime, emphasizing how boundary conditions at the cone's apex influence the scattering amplitude and the importance of observable quantities to distinguish different physical evolutions.

## Contribution

It demonstrates the role of boundary conditions in quantum scattering on a cone and introduces the necessity of observable criteria to identify the chosen evolution.

## Key findings

- Boundary conditions affect the scattering amplitude.
- Purely analytical term arises from boundary conditions.
- Observable quantities are needed to distinguish physical evolutions.

## Abstract

We revisit the scattering of quantum test particles on the conical $(2+1)$-dimensional spacetime and find the scatteting amplitude as a function of the boundary conditions imposed at the appex of the cone. We show that the boundary condition is responsible for a purely analytical term in the scattering amplitude, in addition to those coming from purely topological effects. Since it is possible to have non-equivalent physical evolutions for the wave packet (each one corresponding to a different boundary condition), it seems crucial to have an observable quantity specifying which evolution has been prescribed.