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Homotopy groups and the quantization of localizable systems

Author

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  • Angermann, B.
  • Doebner, H.D.

Abstract

A method of quantization for non-relativistic physical systems S on a Riemannian manifold M is discussed. To characterize the method, we deduce from geometric considerations abstract postulates consistent with the principles laid down by axiomatic quantum mechanics. We construct a large variety of such quantizations and show that this variety is determined by the topology of M. The problem of finding the “correct” quantum description for a system S on M is discussed. Group actions on M lead, inside the given mathematical framework, to systems of imprimitivity on M.

Suggested Citation

  • Angermann, B. & Doebner, H.D., 1982. "Homotopy groups and the quantization of localizable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 433-438.
    • Handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:433-438
    DOI: 10.1016/0378-4371(82)90327-2
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