Lecture Notes on Superconductivity: Condensed Matter and QCD (Lectures at the University of Barcelona, Spain, September-October 2003)
Roberto Casalbuoni∗ Department of Physics of the University of Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy
Florence,
(Dated: October 13, 2003)
Contents I. Introduction A. Basic experimental facts B. Phenomenological models 1. Gorter-Casimir model 2. The London theory 3. Pippard non-local electrodynamics 4. The Ginzburg-Landau theory C. Cooper pairs 1. The size of a Cooper pair D. Origin of the attractive interaction
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II. Effective theory at the Fermi surface A. Introduction B. Free fermion gas C. One-loop corrections D. Renormalization group analysis
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III. The gap equation A. A toy model B. The BCS theory C. The functional approach to the gap equation D. The Nambu-Gor’kov equations E. The critical temperature
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IV. The role of the broken gauge symmetry
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V. Color superconductivity A. Hierarchies of effective lagrangians B. The High Density Effective Theory (HDET) 1. Integrating out the heavy degrees of freedom 2. The HDET in the condensed phase C. The gap equation in QCD D. The symmetries of the superconductive phases 1. The CFL phase 2. The 2SC phase 3. The case of 2+1 flavors 4. Single flavor and single color VI. Effective lagrangians A. Effective lagrangian for the CFL phase B. Effective lagrangian for the 2SC phase VII. NGB and their parameters A. HDET for the CFL phase B. HDET for the 2SC phase C. Gradient expansion for the U (1) NGB in the CFL model and in the 2SC model
∗ Electronic
address:
[email protected]
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