THE RENORMALIZATION-GROUP AND QUANTUM EDGE STATES

The role of edge states in phenomena like the quantum Hall effect is w ell known, and the basic physics has a wide field-theoretic interest. In this paper we introduce a new model exhibiting quantum Hall-like fe atures. We show how the choice of boundary conditions for a one-partic le Schrodinger equation can give rise to states localized at the edge of the system. We consider both the example of a free particle and the more involved example of a particle in a magnetic field. In each case , edge states arise from a non-trivial scaling limit involving the bou ndary condition, and chirality of the boundary condition plays an esse ntial role. Second quantization of these quantum mechanical systems le ads to a multi-particle ground state carrying a persistent current at the edge. We show that the theory quantized with this vacuum displays an ''anomaly'' at the edge which is the mark of a quantized Hall condu ctivity in the presence of an external magnetic field. These models th erefore possess characteristics which make them indistinguishable from the quantum Hall effect at macroscopic distances. We also offer inter pretations for the physics of such boundary conditions which may have a bearing on the nature of the excitations in these models.