Structure of the effective potential in nonrelativistic Chern-Simons field theory

We present the scalar field effective potential for nonrelativistic self-interacting scalar and fermion fields coupled to an Abelian Chern-Simons gauge field. In this model, Gauss's law linearly relates the magnetic field to the matter field densities; hence, we also include radiative effects from the background gauge field. We compute the scalar field effective potential in two gauge families, a gauge reminiscent of the R_ξ gauge in the limit ξ-->0 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 scheme.