Structure of the Effective Potential in Nonrelativistic Chern-Simons Field Theory

Details Structure of the Effective Potential in Nonrelativistic Chern-Simons Field Theory Structure of the Effective Potential in Nonrelativistic Chern-Simons Field Theory

1993-12-13

arxiv.org/abs/hep-th/9312109v1

Phys.Rev. D49 (1994) 5422-5430

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, UdeM-LPN-TH-93-185, CRM-1927

Scientific paper

10.1103/PhysRevD.49.5422

We present the scalar field effective potential for nonrelativistic self-interacting scalar and fermion fields coupled to an Abelian Chern-Simons gauge field. Fermions are non-minimally coupled to the gauge field via a Pauli interaction. Gauss's law linearly relates the magnetic field to the matter field densities; hence, we also include radiative effects from the background gauge field. However, the scalar field effective potential is transparent to the presence of the background gauge field to leading order in the perturbative expansion. We compute the scalar field effective potential in two gauge families. We perform the calculation in a gauge reminiscent of the $R_\xi$-gauge in the limit $\xi\rightarrow 0$ and in the Coulomb family gauges. The scalar field effective potential is the same in both gauge-fixings and is independent of the gauge-fixing parameter in the Coulomb family gauge. The conformal symmetry is spontaneously broken except for two values of the coupling constant, one of which is the self-dual value. To leading order in the perturbative expansion, the structure of the classical potential is deeply distorted by radiative corrections and shows a stable minimum around the origin, which could be of interest when searching for vortex solutions. We regularize the theory with operator regularization and a cutoff to demonstrate that the results are independent of the regularization scheme.

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