No approximate complex fermion coherent states

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

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    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
    Issue number7
    Publication statusPublished - 2007


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


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