Perturbative Expansion in the Galilean Invariant Spin One-Half Chern-Simons Field Theory

TL;DR

This paper develops a Galilean Chern-Simons field theory for two interacting spin-1/2 particles with different masses, analyzing perturbative divergences and their relation to spin configurations, revealing finite results for parallel spins and divergences for antiparallel spins.

Contribution

It introduces a novel Galilean invariant Chern-Simons theory for two distinct mass spin-1/2 particles and analyzes its perturbative properties, including divergence behavior.

Findings

Finite one-loop contributions for parallel spins.

Divergences in antiparallel spin configurations.

Connection to spin-zero divergence characteristics.

Abstract

A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-1/2 fields of distinct masses M and M'. A method for the construction of states containing N particles of mass M and N' particles of mass M' is given which is subsequently used to display equivalence to the spin-1/2 Aharonov-Bohm effect in the N = N' =1 sector of the model. The latter is then studied in perturbation theory to determine whether there are divergences in the fourth order (one loop) diagram. It is found that the contribution of that order is finite (and vanishing) for the case of parallel spin projections while the antiparallel case displays divergences which are known to characterize the spin zero case in field theory as well as in quantum mechanics.