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Supercoherent States—An Introduction

  • Monique Combescure
  • Didier Robert
Part of the Theoretical and Mathematical Physics book series (TMP)

Abstract

In previous chapters we have considered coherent states systems for bosons and for fermions separately. Here we introduce superspaces, where it is possible to consider simultaneously bosons and fermions. Our aim is to give a short introduction to this deep and difficult subject by considering some elementary examples where coherent states and quantization are involved.

Keywords

Coherent State Poisson Bracket Grassmann Variable Dirac Bracket Grassmann Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abe, S., Suzuki, N.: Wigner distribution function of a simple optical model: an extended-phase-space approach. Phys. Rev. A 45, 520–523 (2001) ADSCrossRefGoogle Scholar
  2. 7.
    Arnold, V.: Mathematical Methods of Classical Mechanics. Springer, New York (1999) Google Scholar
  3. 20.
    Berezin, F.A.: General concept of quantization. Commun. Math. Phys. 40, 153–174 (1975) MathSciNetADSCrossRefGoogle Scholar
  4. 22.
    Berezin, F.A.: Introduction to Superanalysis. Reidel, Dordrecht (1987) zbMATHGoogle Scholar
  5. 62.
    De Witt, B.: Supermanifolds. Cambridge University Press, Cambridge (1984) Google Scholar
  6. 65.
    Deligne, P., Etingof, P., Freed, D., Kazhdan, D., Morgan, J., Morrison, D., Witten, E.: Quantum Fields and Strings: a Course for Mathematicians, vol. 1. AMS, Providence (1999) zbMATHGoogle Scholar
  7. 69.
    Dirac, P.A.: Lectures on Quantum Mechanics. Dover, Princeton (2001) Google Scholar
  8. 92.
    Goldstein, H.: Classical Mechanics. Addison-Wesley, Reading (1980) zbMATHGoogle Scholar
  9. 99.
    Hagedorn, G.: Semiclassical quantum mechanics III. Ann. Phys. 135, 58–70 (1981) MathSciNetADSCrossRefGoogle Scholar
  10. 100.
    Hagedorn, G.: Semiclassical quantum mechanics IV. Ann. Inst. Henri Poincaré. Phys. Théor. 42, 363–374 (1985) MathSciNetGoogle Scholar
  11. 105.
    Helein, F.: A representation formula for maps on supermanifolds. J. Math. Phys. 49, 1–19 (2008) MathSciNetCrossRefGoogle Scholar
  12. 112.
    Henneaux, M., Teitelboim, C.: Quantization of Gauge Systems. Princeton University Press, Princeton (1994) Google Scholar
  13. 132.
    Leites, D.A.: Introduction to the theory of supermanifolds. Russ. Math. Surv. 35, 3–57 (1980) MathSciNetzbMATHCrossRefGoogle Scholar
  14. 169.
    Rogers, A.: Supermanifolds. Theory and Applications. World Scientific, Singapore (2007) zbMATHCrossRefGoogle Scholar
  15. 182.
    Takhtajan, L.A.: Quantum mechanics for mathematicians. In: Quantum Mechanics for Mathematicians. Graduate Studies in Mathematics, vol. 95. AMS, Providence (2008) Google Scholar
  16. 184.
    Thaller, B.: The Dirac Operator. Springer, Berlin (1990) Google Scholar
  17. 190.
    Varadarajan, V.S.: Supersymmetry for Mathematicians: An Introduction. Am. Math. Soc., Providence (2004) zbMATHGoogle Scholar
  18. 200.
    Witten, E.: Supersymmetry and Morse theory. J. Differ. Geom. 17, 661–692 (1982) MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Monique Combescure
    • 1
  • Didier Robert
    • 2
  1. 1.Batiment Paul DiracIPNLVilleurbanneFrance
  2. 2.Laboratoire Jean-Leray Departement de MathematiquesNantes UniversityNantes Cedex 03France

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