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.
docType_s : Journal articles
Domain :


http://hal.in2p3.fr/in2p3-00721798
Contributor : Girod Dominique <>
Submitted on : Monday, July 30, 2012 - 2:00:17 PM
Last modification on : Monday, July 30, 2012 - 2:00:17 PM

Identifiers

Collections

Citation

M. Combescure, D. Robert. Fermionic Coherent States. Journal of Physics A: Mathematical and Theoretical, Institute of Physics: Hybrid Open Access, 2012, 45, pp.244005. <10.1088/1751-8113/45/24/244005>. <in2p3-00721798>

Export

Share

Metrics