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Spin‐charge rotating local reference frames: a unified U(2) = U(1) ⊗ SU(2) approach to the interacting electrons
Author(s) -
Kopeć T. K.
Publication year - 2007
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200674612
Subject(s) - electron , spin (aerodynamics) , physics , charge (physics) , special unitary group , quantum mechanics , thermodynamics
A spin‐charge unifying description for the Hubbard model based on the time dependent local gauge transformations is developed. The collective variables for charge and spin are isolated in the form of the space‐time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as a composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. We elaborate on the microscopic origins of the effective action with the Coulomb interaction that contain topological theta terms. Furthermore, we unravel the link between non‐trivial multiply‐connected topological structure of the U(2) = U(1) ⊗ SU(2) configurational space for gauge fields and the instanton contribution to the statistical sum. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)