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

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.

14 pages LaTeX, including 2 figures using epsf

Cited by in corpus (6)

• On the Nonrelativistic Limit of the Scattering of Spin One-half Particles Interacting with a Chern-Simons Field
• Consistency of the Born Approximation for the spin-1/2 Aharonov-Bohm Scattering
• On the Nonabelian Aharonov Bohm Scattering of Spinless Particles
• Partial wave Analysis of the First Order Born Amplitude of a Dirac Particle in an Aharonov-Bohm Potential
• Radiative Corrections to the Aharonov-Bohm Scattering
• On spin-1 massive particles coupled to a Chern-Simons field