Quantizing Chaplygin Hamiltonizable nonholonomic systems

Abstract

AbstractIn this article we develop a quantization procedure for Chaplygin Hamiltonizable nonholonomic systems—mechanical systems subject to non-integrable velocity constraints whose reduced mechanics is Hamiltonian after a suitable time reparametrization—using Poincaré transformations and geometric quantization. We illustrate the theory developed through examples and discuss potential applications to the study of the quantum mechanics of nanovehicles.