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Method of Orbits of Co-Associated Representation in Thermodynamics of the Lie Non-compact Groups

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

A method of the solution of the main problem of homogeneous spaces thermodynamics for non-compact Lie groups is presented in the work. The method originates from formalism of non-commutative Fourier analysis based on method of coadjoint orbits. A formula that allows efficiently evaluate heat kernel and statistic sum on non-compact Lie group is obtained. The algorithm of construction of high temperature heat kernel expansion is also discussed.

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Authors and Affiliations

  1. Omsk State Technical University, 644050, Prospekt Mira, 11/8, Omsk, Russian Federation

    Vitaly Mikheev

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  1. Vitaly Mikheev
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Correspondence to Vitaly Mikheev .

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Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Mikheev, V. (2017). Method of Orbits of Co-Associated Representation in Thermodynamics of the Lie Non-compact Groups. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_50

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

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