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Classical limits of gauge-invariant states and the choice of algebra for strict quantization

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Abstract

We analyze the quantization of a system consisting of a particle in an external Yang–Mills field within a C*-algebraic framework. We show that in both the classical and quantum theories of such a system, the kinematical algebra of physical quantities can be obtained by restricting attention to symmetry-invariant states on a C*-algebra. We use this to show that symmetry-invariant quantum states correspond to symmetry-invariant classical states in the classical limit.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, USA

    Thomas L. Browning

  2. Department of Philosophy, University of Washington, Seattle, USA

    Benjamin H. Feintzeig

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  1. Thomas L. Browning
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  2. Benjamin H. Feintzeig
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Correspondence to Benjamin H. Feintzeig.

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Browning, T.L., Feintzeig, B.H. Classical limits of gauge-invariant states and the choice of algebra for strict quantization. Lett Math Phys 110, 1835–1860 (2020). https://doi.org/10.1007/s11005-020-01278-w

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  • DOI: https://doi.org/10.1007/s11005-020-01278-w

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