MAXWELL-CHERN-SIMONS ELECTRODYNAMICS ON A DISK

The Maxwell-Chern-Simons (MCS) Lagrangian is the Maxwell Lagrangian au gmented 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 d ifferent media. We show that quantization is not unique, but depends o n a nonnegative parameter lambda. 1/lambda is the penetration depth of the fields described by these Lagrangians into the medium in the exte rior of D. For lambda = 0, there are edge observables and edge states localized at the boundary partial derivative D for the MCS system. The y describe the affine Lie group LU(1). Their excitations carry zero en ergy, signifying an infinite degeneracy of all states of the theory. T here is also an additional infinity of single particle excitations of exactly the same energy proportional to Absolute value of k, k being t he strength of the Chern-Simons term. The MCS theory for lambda = 0 ha s the huge symmetry group LU(1) x U(infinity). In the Maxwell theory, the last-mentioned excitations are absent while the edge observables, which exist for lambda = 0, commute. Also, these excitations are descr ibed by states which are not localized at partial derivative D and are characterized by a continuous and infinitely degenerate spectrum. All these degeneracies are lifted and edge observables and their states c ease to exist for lambda > 0. The novel excitations discovered in this paper should be accessible to observations. We will discuss issues re lated to observations, as also the generalization of the present consi derations to vortices, domain walls and monopoles, in a paper under pr eparation.