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
Article

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 

PACS

05.30.Jp 05.30.Fk 42.50.Ar 

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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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