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Pre-quantisation for an arbitrary Abelian structure group

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Abstract

A geometric study of canonical quantisation generalising the pre-quantisation technique of Kostant is presented. The concept of a quantising fibre bundle with an arbitrary abelian structure group arises naturally in this framework. It is demonstrated that quantising fibre bundles induce vector-field representations. Necessary and sufficient conditions for the quantisability of symplectic manifolds are derived and a proof for the existence of two-dimensional non-reducible quantising toral bundles is given.

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  1. Institut für Theoretische Physik der Technischen Universität Clausthal, Clausthal-Zellerfeld, Germany

    J. -E. Werth

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  1. J. -E. Werth
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Werth, J.E. Pre-quantisation for an arbitrary Abelian structure group. Int J Theor Phys 12, 183–190 (1975). https://doi.org/10.1007/BF01807762

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  • DOI: https://doi.org/10.1007/BF01807762

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