Abstract
Feynman’s path integral representation of the covariant quantum mechanical propagator entails Schwinger’s dynamical variational principle as shown by DeWitt. On one hand we discuss the covariant quantum Hamiltonian obtained from Schwinger’s principle in curved space, following Kawai. On the other hand we present a novel Fourier series analysis of the path integral itself. The resulting Hamiltonian is identical to Kawai’s. For the ‘free particle’ the Hamiltonian involves a quantum mechanical curvature scalar potential v=ħ2R/8.
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© 1980 Plenum Press, New York
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Dekker, H. (1980). Quantization in Curved Spaces. In: Antoine, JP., Tirapegui, E. (eds) Functional Integration. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-7035-6_15
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DOI: https://doi.org/10.1007/978-1-4615-7035-6_15
Publisher Name: Springer, Boston, MA
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