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Fédération Denis Poisson |  |
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Fédération Denis Poisson | |
| HAL: hal-00667316, version 1 |
| arXiv: 1111.3656 |
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| Symmetries and currents of the ideal and unitary Fermi gases |
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| Xavier Bekaert 1, 2Elisa Meunier 1, 2 |
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| (2012-02-06) |
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| The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite dimensional extension of the Schroedinger algebra, it is isomorphic to the Weyl algebra of quantum observables, and it may be interpreted as a non-relativistic higher-spin algebra. The associated infinite collection of Noether currents bilinear in the fermions are derived from their relativistic counterparts via a light-like dimensional reduction. The minimal coupling of these currents to background sources is rewritten in a compact way by making use of Weyl quantisation. Pushing forward the similarities with the holographic correspondence between the minimal higher-spin gravity and the critical O(N) model, a putative bulk dual of the unitary and the ideal Fermi gases is discussed. |
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| 1: | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| 2: | Fédération de recherche Denis Poisson (FRDP) |
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CNRS : FR2964 – Université d'Orléans – Université François Rabelais - Tours |
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| 3: | Institut für Theoretische Physik |
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Universität Heidelberg |
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| 4: | Department of Physics |
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University of Washington |
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| Subject | : | Physics/High Energy Physics - Theory Physics/Condensed Matter/Quantum Gases |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1111.3656 |
| hal-00667316, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00667316 | |
| oai:hal.archives-ouvertes.fr:hal-00667316 | |
| From: Elisa Meunier | |
| Submitted on: Tuesday, 7 February 2012 14:06:02 | |
| Updated on: Thursday, 21 February 2013 10:15:28 | |
