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arXiv · 1009.4071

Dimensional reduction in quantum field theories at finite temperature and density

Johannes Hofmann
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Abstract

In this work we present two correspondences between the massless Gross-Neveu model with one or two coupling constants in 1+1 dimensions and nonrelativistic field theories in 3+1 dimensions. It is shown that on a mean-field level the massless Gross-Neveu model can be mapped onto BCS theory provided that translational invariance of the condensate is assumed. The generalized massless Gross-Neveu model with two coupling constants is mapped onto a quasi one-dimensional extended Hubbard model used in the description of spin-Peierls systems. It is shown that the particle hole symmetry of the Hubbard model implies self-consistency of the condensate. The dimensional reduction allows an identification of the phase diagrams of the models.

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Johannes Hofmann. 2010-12-16. Dimensional reduction in quantum field theories at finite temperature and density. https://doi.org/10.1103/physrevd.82.125027

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