CHERN-SIMONS THEORY OF SCALAR PARTICLES AND THE AHARONOV-BOHM EFFECT

The S-matrix of the relativistic theory of charged scalar particles in teracting via the Chern-Simons field is shown to be formally equivalen t to the S-matrix of scalar QED in 2 + 1 dimensions in which the Feynm an diagrams with external photon lines are excluded and the propagator s of the Chern-Simons particles are substituted instead of the photon propagators. It is shown that the non-relativistic limit of the scatte ring amplitude of two anyons is also finite independently of the prese nce of the contact interaction, unlike the non-relativistic theory. It is found that for a certain value of the contact interaction, the sca ttering amplitude coincides with that of Aharonov-Bohm scattering in t he same approximation.