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| Titre : |
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Fermionic Coherent States |
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| Auteur : |
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M. Combescure1, D. Robert2 |
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| Laboratoire : |
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| Résumé : |
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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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| Type de publication : |
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Articles dans des revues avec comité de lecture |
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Date de publication
ou d'écriture : |
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2012 |
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| Nom du périodique : |
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| Journal of Physics A: Mathematical and Theoretical |
| Publisher |
Institute of Physics: Hybrid Open Access |
| ISSN |
1751-8113 (eISSN : 1751-8121) |
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| Volume : |
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45 |
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| Page/Article : |
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244005 |
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