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Covariant geometric quantization of nonrelativistic time-dependent mechanics (2002)

Giachetta, G. ; Mangiarotti, L.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 43 (2002), S. 56-68

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: We provide geometric quantization of the vertical cotangent bundle V*Q→Q→R, equipped with the canonical Poisson structure and treated as a momentum phase space of nonrelativistic time-dependent mechanics. We show that this quantization is equivalent to fiberwise quantization of symplectic fibers of V*Q→R and that the quantum algebra of time-dependent mechanics is an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra and describes quantum evolution in time-dependent mechanics as a parallel transport. © 2002 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.1412597

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