AHARONOV-BOHM SCATTERING IN CHERN-SIMONS THEORY OF SCALAR PARTICLES

The S-matrix operator for relativistic theory of charged scalar partic les interacting via Chern-Simons field is constructed and is shown to be formally the same as the S-matrix in relativistic scalar quantum el ectrodynamics in which the Feynman diagrams with external photon lines are not considered and the propagators of the Chern-Simons particles are substituted in place of the ones for photons. All the one-loop Fey nman diagrams for relativistic scattering amplitude of two charged par ticles are calculated. Due to the renormalizability of the theory only two diagrams have linear divergence, which are regularized. The nonre lativistic limit of the scattering amplitude is also finite, unlike th e non-relativistic Chern-Simons scattering theory. It is found that fo r a certain value of the contact interaction, corresponding to the rep ulsive case, the scattering amplitude coincides with that of Aharonov- Bohm scattering, in the same approximation. (C) 1996 Academic Press, I nc.