Bosonization rules in 12 + 1 dimensions |
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| Institution: | 1. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080, USA;2. Department of Physics, Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, UK;3. Departament d''Estructura i Constituents de la Matéria, Facultat de Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain;1. School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China;2. School of Mathematics and Statistics, Pu''er University, Yunnan 665000, China;1. Philippe Meyer Institute, Physics Department, École Normale Supérieure, PSL Research University, 24 rue Lhomond, F-75231 Paris Cedex 05, France;2. University of Graz, Institute for Physics, A-8010 Graz, Austria;1. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland;2. Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, Nussallee 14-16, D-53115 Bonn, Germany;3. Tbilisi State University, 0186 Tbilisi, Georgia |
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| Abstract: | We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure. |
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