The fermion density operator in the droplet bosonization picture |
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| Institution: | 1. Departamento de Física Teórica II, Universidad Complutense, 28040 Madrid, Spain;2. Physics Department, City College of the CUNY, New York, NY 10031, USA;1. Institut de Physique Théorique, CEA Saclay, F-91191 Gif-sur-Yvette, France;2. Mathematical Physics Laboratory, RIKEN Nishina Center, Saitama 351-0198, Japan;3. Institute of Physics AS CR, Na Slovance 2, Prague 8, Czech Republic;1. Teoretisk fysik, Karlstads Universitet, Universitetsgatan 21, S-65188, Karlstad, Sweden;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G2G1, Canada;3. Fakultät für Mathematik, Universität Wien, Austria;4. Fachbereich Mathematik, Universität Hamburg, Bereich Algebra und Zahlentheorie, Bundesstraße 55, D-20146 Hamburg, Germany;1. Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague 186 75, Czech Republic;2. Jacobs University Bremen, 28759 Bremen, Germany;3. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Prague 115 19, Czech Republic;1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 1(2), Leninskie gory, Moscow 119991, Russian Federation;2. Institut für Theoretische Teilchenphysik, Karlsruher Institut für Technologie (KIT), D-76128 Karlsruhe, Germany |
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| Abstract: | We derive the phase space particle density operator in the ‘droplet’ picture of bosonization in terms of the boundary operator. We demonstrate that it satisfies the correct algebra and acts on the proper Hilbert space describing the underlying fermion system, and therefore it can be used to bosonize any Hamiltonian or related operator. As a demonstration we show that it reproduces the correct excitation energies for a system of free fermions with arbitrary dispersion relations. |
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