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.
Highlights
A great effort in the nuclear and hadron physics community has been put into constructing the scattering dynamics of few-particle interactions from the discrete bound state energy spectrum that is computed in various types of traps, such as the commonly used periodic finite box in lattice QCD (LQCD) and the harmonic oscillator trap in nuclear physics computation
The ultimate goal is to study and explore the nature of particle interactions that plays an essential role in many fields of physical science, such as nuclear physics and astrophysics
Relating the energy shift caused by particle interactions to the on-shell scattering parameters such as phase shift has a long history across many fields in physics
Summary
A great effort in the nuclear and hadron physics community has been put into constructing the scattering dynamics of few-particle interactions from the discrete bound state energy spectrum that is computed in various types of traps, such as the commonly used periodic finite box in lattice QCD (LQCD) and the harmonic oscillator trap in nuclear physics computation. Regardless of the difference among various traps, the same strategy is shared: as the two physical scales are clearly separated, a closed asymptotic form can be found, in which short-range dynamics is described by a scattering phase shift and the long-range effect is given by an analytic form that describes how the propagation of particles is affected by the trap, e.g., Lüscher’s zeta function in a periodic boundary condition.
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