Inequivalent Representations of Commutator or Anticommutator Rings of Field Operators and Their Applications |
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Authors: | M Matejka M Noga |
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Institution: | (1) Department of Chemical Physics, Faculty of Mathematics, Physics and Computer Sciences, Comenius University, Mlynská Dolina, 842 48 Bratislava, Slovakia;(2) Department of Theoretical Physics, Faculty of Mathematics, Physics and Computer Sciences, Comenius University, Mlynská Dolina, 842 48 Bratislava, Slovakia |
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Abstract: | Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely
many inequivalent representations of the canonical commutator or anticommutator rings of field operators. This implies that
the system can theoretically exist in infinitely many Gibbs states. The system resides in the Gibbs state which corresponds
to its minimal Helmholtz free energy at a given range of the thermodynamic variables. Individual inequivalent representations
are associated with different thermodynamic phases of the system. The BCS Hamiltonian of superconductivity is chosen to be
an explicit example for the demonstration of the important role of inequivalent representations in practical applications.
Its analysis from the inequivalent representations’ point of view has led to a recognition of a novel type of the superconducting
phase transition.
PACS: 03.70.+k, 05.30.−d, 11.10.−z, 74.20.Fg, 74.25.Bt, 74.78.Bz |
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Keywords: | inequivalent representations BCS model superconductivity thermodynamic properties layered structures Uemura plot |
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