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arXiv · hep-th/9910107

Stochastic field theory for a Dirac particle propagating in gauge field disorder

T. Guhr·T. Wilke·H. A. Weidenmueller
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Abstract

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.

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T. Guhr, T. Wilke, H. A. Weidenmueller. 1999-10-14. Stochastic field theory for a Dirac particle propagating in gauge field disorder. https://doi.org/10.1103/physrevlett.85.2252

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