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Fermionic Coherent States

Abstract : The aim of this paper is to give a self-contained and unified presentation of a fermionic coherent state theory with the necessary mathematical details, discussing their definition, properties and some applications. After defining Grassmann algebras, it is possible to get a classical analog for the fermionic degrees of freedom in a quantum system. Following the basic work of Berezin (1966 The Method of Second Quantization (New York: Academic); 1987 Introduction to Superanalysis (Dordrecht: Reidel Publishing Company)), we show that we can compute with Grassmann numbers as we do with complex numbers: derivation, integration, Fourier transform. After that we show that we have quantization formulas for fermionic observables. In particular, there exists a Moyal product formula. As an application, we consider explicit computations for propagators with quadratic Hamiltonians in annihilation and creation operators. We prove a Mehler formula for the propagator and Mehlig-Wilkinson-type formulas for the covariant and contravariant symbols of 'metaplectic' transformations for fermionic states.
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Contributor : Dominique Girod Connect in order to contact the contributor
Submitted on : Monday, July 30, 2012 - 2:17:52 PM
Last modification on : Tuesday, September 21, 2021 - 4:06:02 PM

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M. Combescure, D. Robert. Fermionic Coherent States. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2012, 45, pp.244005. ⟨10.1088/1751-8113/45/24/244005⟩. ⟨in2p3-00721798⟩



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