NONRELATIVISTIC FERMIONS INTERACTING THROUGH THE CHERN-SIMONS FIELD AND THE AHARONOV-BOHM SCATTERING-AMPLITUDE

Starting from the non-relativistic field theory of spin-A fermions int eracting through the Abelian Chem-Simons term, we show that the quanti zed field theory leads, in the two-particle sector, to a two-particle Aharonov-Bohm-like Schrodinger equation with an antisymmetric (fermion ic) wavefunction and without a delta function term. Calculating pertur batively the field-theoretic two-particle scattering amplitude up to o ne-loop older. we show that, in contrast to the scalar theory, the con tribution of all the one-loop diagrams is finite and null, and that of the tree level ones coincides with the exact amplitude. Further, the Pauli matter-magnetic field interaction term is shown not to contribut e to the amplitude to this order.