Quantization of Bogomol'nyi soliton dynamics

TL;DR

This paper analytically approximates the low-energy scattering cross-section of BPS SU(2) magnetic monopoles using the geodesic approximation and zeta function techniques, showing good agreement with numerical results.

Contribution

It introduces an analytical method for calculating the semi-classical scattering cross-section of monopoles, extending previous numerical approaches.

Findings

Semi-classical cross-section matches numerical results.

Analytic series converges via zeta function continuation.

Agreement observed over a wide range of angles.

Abstract

We approximate analytically the semi-classical differential cross-section for low-energy solitonic BPS SU(2) magnetic monopoles using the geodesic approximation. The semi-classical scattering amplitude, f(\theta), can be expressed as a conditionally convergent infinite series which is made absolutely convergent by analytic continuation of the generalised zeta function. Our results suggest that the classical solitonic cross-section (computed numerically in hep-th:9209063) and the semi-classical cross-section are in good agreement over a wide range of scattering angles, \pi/3<\theta<\pi/2 and \pi/2<\theta<2\pi/3.