Charged particles interaction in both a finite volume and a uniform magnetic field

TL;DR

This paper develops a formalism to analyze charged particle interactions within a finite volume and uniform magnetic field, deriving a quantization condition similar to L"uscher's formula for short-range interactions.

Contribution

It introduces a new formalism that separates short-range physics from finite volume effects in the presence of a magnetic field, leading to a L"uscher-like quantization condition.

Findings

Factorization between short-range and finite volume effects established

Derived a L"uscher-like quantization condition for charged particles in magnetic fields

Formalism applicable to systems with short-range interactions

Abstract

A formalism for describing charged particles interaction in both a finite volume and a uniform magnetic field is presented. In the case of short-range interaction between charged particles, we show that the factorization between short-range physics and finite volume long-range correlation effect is possible, a L\"uscher formula-like quantization condition is thus obtained.