STRUCTURE OF THE EFFECTIVE POTENTIAL IN NONRELATIVISTIC CHERN-SIMONS FIELD-THEORY

We present the scalar field effective potential for nonrelativistic se lf-interacting scalar and fermion fields coupled to an Abelian Chem-Si mons gauge field. In this model, Gauss's law linearly relates the magn etic field to the matter field densities; hence, we also include radia tive effects from the background gauge field. We compute the scalar fi eld effective potential in two gauge families, a gauge reminiscent of the R(xi) gauge in the limit xi --> and in the Coulomb family gauges. We regularize the theory with operator regularization and a cutoff to demonstrate that the results are independent of the regularization sch eme.