On the Nonrelativistic Limit of the Scattering of Spin One-half Particles Interacting with a Chern-Simons Field

Abstract

Starting from a relativistic quantum field theory, we study the low energy scattering of two fermions of opposite spins interacting through a Chern-Simons field. Using the Coulomb gauge we implement the one loop renormalization program and discuss vacuum polarization and magnetic moment effects. We prove that the induced magnetic moments for spin up and spin down fermions are the same. Next, using an intermediary auxiliary cutoff the scattering amplitude is computed up to one loop. Similarly to Aharonov-Bohm effect for spin zero particles, the low energy part of the amplitude contains a logarithmic divergence in the limit of very high intermediary cutoff. In our approach however the needed counterterm is automatically provided without any additional hypothesis.

12 pages, 2 figures, revtex; Minor corrections

References in corpus (2)

• Perturbative Expansion in the Galilean Invariant Spin One-Half Chern-Simons Field Theory
• The Low Energy Limit of the Chern-Simons Theory Coupled to Fermions

Cited by in corpus (8)

• Aharonov-Bohm Effect in Cyclotron and Synchrotron Radiations
• Noncommutative Field Theory: Nonrelativistic Fermionic Field Coupled to the Chern-Simons Field in 2+1 Dimensions
• On the Nonabelian Aharonov Bohm Scattering of Spinless Particles
• Radiative Corrections to the Aharonov-Bohm Scattering
• Non-Abelian Aharonov-Bohm Scattering of Spin 1/2 Particles
• Classical limit for the scattering of Dirac particles in a magnetic field
• On spin-1 massive particles coupled to a Chern-Simons field
• Relativistic scalar Aharonov-Bohm scattering