Summary
Using the projection operator method, the quantization of a dynamical system constrained to a curved space embedded in the higher-dimensional Euclidean space is investigated in the framework of the canonical formalism. We show that the resultant Hamiltonian contains the quantum correction term, which is completely missed in the usual approach with Dirac’s formalism.
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Nakamura, M., Minowa, H. Quantum theory on a curved space. Nuov Cim B 108, 1181–1190 (1993). https://doi.org/10.1007/BF02827314
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DOI: https://doi.org/10.1007/BF02827314