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Method of orbits of coassociated representation in thermodynamics of the lie noncompact groups

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Abstract

In the present paper, an efficient method of solving the main problem of thermodynamics of homogeneous spaces is presented. The method is based on the formalism of the noncommutative harmonic analysis relying on the method of orbits of coassociated representation. In the present work, the formula is derived that allows one to construct effectively the density matrix and the statistical sum in space of any arbitrary generally noncompact non-unimodular Lie group. To illustrate the method, an example is given of exact calculation of the statistical sum and density matrix in the Riemannian space of the noncompact Lie group with left-invariant metric.

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References

  1. N. Heart, Geometrical Quantization in Action [Russian translation], Nauka, Moscow (1984).

    Google Scholar 

  2. S. Minakshisundaram and A. Pleijel, Can. J. Math., 1, 242–256 (1949).

    MATH  Google Scholar 

  3. S. R. S. Varadhan, Comm. Pure Appl. Math., 20, 431–455 (1967).

    Article  MATH  Google Scholar 

  4. V. F. Molchanov, Usp. Matem. Nauk, 30, No. 6, 1–64 (1975).

    MATH  Google Scholar 

  5. V. V. Mikheev and I. V. Shirokov, Russ. Phys. J., No. 1, 6–14 (2003).

  6. V. V. Mikheev and I. V. Shirokov, Electr. J. Theor. Phys., 2, No. 7, 1–10 (2005).

    MATH  Google Scholar 

  7. I. V. Shirokov, Theor. Matem. Fiz., 123, No. 3, 407–423 (2000).

    Google Scholar 

  8. A. A. Kirillov, Elements of Representation Theory [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  9. A. Barut and R. Ronchka, Theory of Group Representations and Its Applications [in Russian], Ainshtain, Bishkek (1997).

    Google Scholar 

  10. S. P. Baranovskii, V. V. Mikheev, and I. V. Shirokov, Teor. Matem. Fiz., 129, No. 1, 3–14 (2001).

    Google Scholar 

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Authors and Affiliations

  1. Omsk State University, Russia

    V. V. Mikheev & I. V. Shirokov

Authors
  1. V. V. Mikheev
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  2. I. V. Shirokov
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Correspondence to V. V. Mikheev.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 84–88, March, 2007.

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Mikheev, V.V., Shirokov, I.V. Method of orbits of coassociated representation in thermodynamics of the lie noncompact groups. Russ Phys J 50, 290–295 (2007). https://doi.org/10.1007/s11182-007-0040-5

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  • DOI: https://doi.org/10.1007/s11182-007-0040-5

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