"Topological" (Chern-Simons) quantum mechanics

Abstract

We construct quantum-mechanical models that are analogs of three-dimensional, topologically massive as well as Chern-Simons gauge-field theories, and we study the phase-space reductive limiting procedure that takes the former to the latter. The zero-point spectra of operators behave discontinuously in the limit, as a consequence of a nonperturbative quantum-mechanical anomaly. The nature of the limit for wave functions depends on the representation, but is always such that normalization is preserved.