The fermion-fermion effective potential in the maxwell-chern-simons theory

Abstract

The effective nonrelativistic potential VT describing the fermion-fermion interaction in the Maxwell-Chern-Simons theory is derived to the lowest order in perturbation theory. As expected, VT is not invariant under parity and time-reversal transformations. The quantum dynamics generated by Vr becomes exactly solvable at the limits where either the Maxwell or the Chern- Simons terms disappear; in neither case electron-electron bound states show up. However, numerical calculations indicate that fermion-fermion bound states do exist in the general case.