Advertisement

Russian Physics Journal

, Volume 61, Issue 3, pp 556–565 | Cite as

Noncommutative Reduction of the Bloch Equation in the Heisenberg–Weyl Group

  • D. A. Ivanov
  • A. I. Breev
Article

The Bloch equation in the Heisenberg–Weyl group is considered. A λ-representation of the Lie algebra of a Heisenberg–Weyl group of arbitrary dimensionality is constructed, and an expression for the statistical sum in the Heisenberg–Weyl group is obtained. Expressions for the statistical sum of the Heisenberg–Weyl group and other thermodynamic quantities are analyzed.

Keywords

noncommutative integration method thermodynamics of homogeneous spaces Heisenberg–Weyl group statistical sum 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. V. Vassilevich, Phys. Rep., 388, No. 5, 279–360 (2003).ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    S. Giombi, A. Maloney, and X. Yin, J. High Energy Phys., 2008, No. 08, 007 (2008).ADSCrossRefGoogle Scholar
  3. 3.
    J. R. David, M. R. Gaberdiel, and R. Gopakumar, J. High Energy Phys., 2010, No. 4, 125 (2010).CrossRefGoogle Scholar
  4. 4.
    N. Berline, E. Getzler, and M. Vergne, Heat Kernels and Dirac Operators, Springer-Verlag, Berlin (2003).zbMATHGoogle Scholar
  5. 5.
    N. Hart, Geometric Quantization in Action, D. Reidel Publishing Co., Dordrecht (1983).CrossRefGoogle Scholar
  6. 6.
    J. Lott., J. Diff. Geom., No. 35, 471–510 (1992).CrossRefGoogle Scholar
  7. 7.
    E. Bueler, Trans. Am. Math. Soc., 351, No. 2, 683–713 (1999).MathSciNetCrossRefGoogle Scholar
  8. 8.
    V. V. Mikheev and I. V. Shirokov, Russ. Phys. J., 50, No. 3, 290–295 (2007).CrossRefGoogle Scholar
  9. 9.
    V. V. Mikheev and I. V. Shirokov, Russ. Phys. J., 46, No. 1, 6–14 (2003).CrossRefGoogle Scholar
  10. 10.
    O. Calin, D. C. Chang, K. Furutani, and C. Iwasaki, Heat Kernels for Elliptic and Sub-elliptic Operators, Springer, New York (2010).zbMATHGoogle Scholar
  11. 11.
    A. A. Magazev, V. V. Mikheyev, and I. V. Shirokov, SIGMA, No. 11, 66–17 (2015).Google Scholar
  12. 12.
    I. V. Shirokov, K-Orbits, Harmonic Analysis in Homogeneous Spaces, and Integration of Differential Equations [in Russian], Preprint, Omsk State University, Omsk (1998).Google Scholar
  13. 13.
    A. A. Magazev, TSPU Bulletin, No. 12 (153), 152–157 (2014).Google Scholar
  14. 14.
    V. G. Bagrov, V. V. Belov, V. N. Zadorozhnyi, and A. Yu. Trifonov, Methods of Mathematical Physics: I. Principles of Complex Analysis, II. Elements of Variational Calculus and the Theory of Generalized Functions [in Russian], NTL Publishing House, Tomsk (2002).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Research Tomsk State UniversityTomskRussia

Personalised recommendations