Bardeen, Cooper and Schrieffer in their paper on the theory of superconductivity introduced a model of interacting fermions (BCS model) in which the (instantaneous) interaction is only between electrons of opposite momentum and spin (Cooper pairs). Subsequently it was claimed that in the thermodynamic limit the BCS model is equivalent to the (exactly solvable) quadratic mean field BCS model in which the phenomenon of mass generation is present; a rigorous proof of this equivalence is however still an open problem. In this paper we consider an interacting fermionic model in which the Cooper pairs interact through a finite range time dependent interaction. For this model (quartic in the fermions and not solvable) we are able to prove the generation of mass in the thermodynamic limit and its equivalence with the mean field BCS model. The proof is achieved by a convergent perturbation expansion about mean field theory.

Mastropietro, V. (2007). Mass generation in a fermionic model with finite range time dependent interactions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 269(2), 401-424 [10.1007/s00220-006-0093-2].

Mass generation in a fermionic model with finite range time dependent interactions

MASTROPIETRO, VIERI
2007-01-01

Abstract

Bardeen, Cooper and Schrieffer in their paper on the theory of superconductivity introduced a model of interacting fermions (BCS model) in which the (instantaneous) interaction is only between electrons of opposite momentum and spin (Cooper pairs). Subsequently it was claimed that in the thermodynamic limit the BCS model is equivalent to the (exactly solvable) quadratic mean field BCS model in which the phenomenon of mass generation is present; a rigorous proof of this equivalence is however still an open problem. In this paper we consider an interacting fermionic model in which the Cooper pairs interact through a finite range time dependent interaction. For this model (quartic in the fermions and not solvable) we are able to prove the generation of mass in the thermodynamic limit and its equivalence with the mean field BCS model. The proof is achieved by a convergent perturbation expansion about mean field theory.
2007
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - FISICA MATEMATICA
English
Con Impact Factor ISI
RENORMALIZATION-GROUP; FIELD THEORY; SUPERCONDUCTIVITY; PERTURBATION; EXPANSION; SYSTEMS; LIQUID
http://www.springerlink.com/content/x351106729748365/
Mastropietro, V. (2007). Mass generation in a fermionic model with finite range time dependent interactions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 269(2), 401-424 [10.1007/s00220-006-0093-2].
Mastropietro, V
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/34037
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