MAXWELL-CHERN-SIMONS ELECTRODYNAMICS ON A DISK

Abstract

The Maxwell-Chern-Simons (MCS) Lagrangian is the Maxwell Lagrangian augmented by the Chern-Simons term. In this paper, we study the MCS and Maxwell Lagrangians on a disk D. They are of interest for the quantum Hall effect, and also when the disk and its exterior are composed of different media. We show that quantization is not unique, but depends on a nonnegative parameter λ. 1/λ is the penetration depth of the fields described by these Lagrangians into the medium in the exterior of D. For λ=0, there are edge observables and edge states localized at the boundary ∂D for the MCS system. They describe the affine Lie group [Formula: see text]. Their excitations carry zero energy, signifying an infinite degeneracy of all states of the theory. There is also an additional infinity of single particle excitations of exactly the same energy proportional to |k|, k being the strength of the Chern-Simons term. The MCS theory for λ=0 has the huge symmetry group [Formula: see text]. In the Maxwell theory, the last-mentioned excitations are absent while the edge observables, which exist for λ=0, commute. Also, these excitations are described by states which are not localized at ∂D and are characterized by a continuous and infinitely degenerate spectrum. All these degeneracies are lifted and edge observables and their states cease to exist for λ>0. The novel excitations discovered in this paper should be accessible to observations. We will discuss issues related to observations, as also the generalization of the present considerations to vortices, domain walls and monopoles, in a paper under preparation.