Quantization of a nonholonomic system. (English) Zbl 1228.81194
Summary: We consider the problem of quantizing a nonholonomic system. This is highly nontrivial since such a system, which is subject to nonholonomic constraints, is not variational (or Hamiltonian). Our approach is to couple the system to a field which enforces the constraint in a suitable limit. We consider a simple but representative nonholonomic system, the Chaplygin sleigh. We then quantize the full (Hamiltonian) system. This system exhibits a key complicating feature of some nonholonomic systems – internal dissipative dynamics.
MSC:
| 81S10 | Geometry and quantization, symplectic methods |
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