No approximate complex fermion coherent states

Tomas Tyc, Brett Hamilton, Barry Cyril C. Sanders, William D Oilver

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)1027-1048
Number of pages22
JournalFoundations of Physics
Volume37
Issue number7
DOIs
Publication statusPublished - 2007

Keywords

  • Coherent state
  • Correlator
  • Factorization
  • Fermion field
  • Grassmann numbers

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