Time-dependent quantum scattering in 2+1 dimensional gravity

TL;DR

This paper analyzes how localized wave packets scatter in a conical spacetime caused by a point mass in 2+1 dimensional gravity, revealing finite scattering amplitudes and drawing parallels with diffraction phenomena.

Contribution

It provides a detailed calculation of scattering amplitudes in 2+1D gravity and highlights the interference effects leading to finite results along classical directions.

Findings

Scattering amplitude is finite along classical directions.

Interference between scattered and transmitted waves explains finiteness.

Analogy with diffraction theory enhances understanding of wave behavior.

Abstract

The propagation of a localized wave packet in the conical space-time created by a pointlike massive source in 2+1 dimensional gravity is analyzed. The scattering amplitude is determined and shown to be finite along the classical scattering directions due to interference between the scattered and the transmitted wave functions. The analogy with diffraction theory is emphasized.