Foundations of Physics

, Volume 37, Issue 7, pp 1027–1048 | Cite as

No Approximate Complex Fermion Coherent States

  • Tomáš Tyc
  • Brett Hamilton
  • Barry C. Sanders
  • William D. Oliver

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.

Key words

coherent state fermion field correlator factorization Grassmann numbers 


05.30.Jp 05.30.Fk 42.50.Ar 


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  1. Signal A.I., Zülicke U. (2005). Appl. Phys. Lett. 87: 102102CrossRefGoogle Scholar
  2. Sudarshan E.C.G. (1963). Phys. Rev. Lett. 10: 277zbMATHCrossRefADSMathSciNetGoogle Scholar
  3. Glauber R.J. (1963). Phys. Rev. 130: 2529CrossRefADSMathSciNetGoogle Scholar
  4. Glauber R.J. (1963). Phys. Rev. 131: 2766CrossRefADSMathSciNetGoogle Scholar
  5. Klauder J.R. (1966). Phys. Rev. Lett. 16: 534CrossRefADSMathSciNetGoogle Scholar
  6. J. L. Martin, Proc. Roy. Soc. Lond. A 251, 543 (1959); Y. Ohnuki and T. Kashiwa, Prog. Theor. Phys. 60, 548 (1978); J. R. Klauder and B.-S. Skagerstam, Coherent States (World Scientific, Singapore, 1985).Google Scholar
  7. Berezin F.A. (1966). The Method of Second Quantization. Academic Press, New YorkzbMATHGoogle Scholar
  8. Schwinger J. (1953). Phys. Rev. 92: 1283CrossRefADSMathSciNetGoogle Scholar
  9. Cahill K.E. and Glauber R.J. (1999). Phys. Rev. A 59: 1538CrossRefADSGoogle Scholar
  10. Aharonov Y., Falkoff D., Lerner E., Pendleton H. (1966). Ann. Phys. (N.Y.) 39: 498CrossRefADSGoogle Scholar
  11. Titulaer U.M., Glauber R.J. (1965). Phys. Rev. 140: B676CrossRefADSMathSciNetGoogle Scholar
  12. Titulaer U.M. and Glauber R.J. (1966). Phys. Rev. 145: 1041CrossRefADSGoogle Scholar
  13. H. P. Yuen and J.H. Shapiro, in Coherence and Quantum Optics IV, edited by L. Mandel and E. Wolf (Plenum, New York, 1978), p. 719.Google Scholar
  14. Tyc T. and Sanders B.C. (2004). J. Phys. A: Math. Gen. 37: 7341zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. Saito S., Endo J., Kodama T., Tonomura A., Fukuhara A., and Ohbayashi K. (1992). Phys. Lett. A 162: 442CrossRefADSGoogle Scholar
  16. Büttiker M. (1992). Phys. Rev. B 46: 12485CrossRefADSGoogle Scholar
  17. Beenakker C.W.J. and Büttiker M. (1992). Phys. Rev. B 46: 1889CrossRefADSGoogle Scholar
  18. Liu R.C. and Yamamoto Y. (1994). Phys. Rev. B 49: 10520CrossRefADSGoogle Scholar
  19. Liu R.C. and Yamamoto Y. (1994). Phys. Rev. B 50: 17411CrossRefADSGoogle Scholar
  20. Aguado R. and Kouwenhoven L.P. (2000). Phys. Rev. Lett. 84: 1986CrossRefADSGoogle Scholar
  21. Mandel L., Wolf E. (1995). Optical Coherence and Quantum Optics. Cambridge University Press, CambridgeGoogle Scholar
  22. R. Glauber, in it Quantum Optics, edited by S. Kay and A. Maitland (Academic Press, New York, 1970), p. 53.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Tomáš Tyc
    • 1
  • Brett Hamilton
    • 2
  • Barry C. Sanders
    • 2
    • 3
  • William D. Oliver
    • 4
  1. 1.Institute of Theoretical PhysicsMasaryk UniversityBrnoCzech Republic
  2. 2.Institute for Quantum Information ScienceUniversity of CalgaryCalgaryCanada
  3. 3.Australian Centre of Excellence for Quantum Computer TechnologyMacquarie UniversitySydneyAustralia
  4. 4.MIT Lincoln LaboratoryLexingtonUSA

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