Non-relativistic fermions interacting through the Chern-Simons field and the Aharonov-Bohm scattering amplitude
V.Ya. Fainberg, Namik Kemal Pak, M. S. Shikakhwa
Starting from the non-relativistic field theory of spin- fermions interacting through the Abelian Chern-Simons term, we show that the quantized field theory leads, in the two-particle sector, to a two-particle Aharonov-Bohm-like Schrödinger equation with an antisymmetric (fermionic) wavefunction and without a delta function term. Calculating perturbatively the field-theoretic two-particle scattering amplitude up to one-loop order, we show that, in contrast to the scalar theory, the contribution 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 contribute to the amplitude to this order.
Journal of Physics A Mathematical and General•Apr 17, 1998•4 citations