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Stochastic evolution of Yang-Mills connections on the noncommutative two-torus

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Abstract

We study quantum stochastic parallel transport processes where the noise terms arise from quantum Brownian motion in Fock space and the connection is chosen to minimize the Yang-Mills functional on a Heisenberg module over the smooth algebra of the noncommutative two-torus. Each such process yields a dilation of a quantum dynamical semigroup whose action on components of the connection induces a family of transformations of the moduli space. From a physical point of view, this describes a highly singular interaction between quantized Yang-Mills fields and the free boson field.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Operations Research, Trent Polytechnic, NG1 4BU, Nottingham, England

    David Applebaum

  2. Forschungszentrum BiBoS, Universität Bielefeld, D-4800, Bielefeld 1, F.R.G.

    David Applebaum

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  1. David Applebaum
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Applebaum, D. Stochastic evolution of Yang-Mills connections on the noncommutative two-torus. Letters in Mathematical Physics 16, 93–99 (1988). https://doi.org/10.1007/BF00402015

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  • DOI: https://doi.org/10.1007/BF00402015

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