No Approximate Complex Fermion Coherent States
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 wordscoherent state fermion field correlator factorization Grassmann numbers
PACS05.30.Jp 05.30.Fk 42.50.Ar
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- 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
- 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
- Mandel L., Wolf E. (1995). Optical Coherence and Quantum Optics. Cambridge University Press, CambridgeGoogle Scholar
- R. Glauber, in it Quantum Optics, edited by S. Kay and A. Maitland (Academic Press, New York, 1970), p. 53.Google Scholar