Lecture Notes on Superconductivity: Condensed Matter and QCD: https://arxiv.org/abs/1810.11125

Roberto Casalbuoni

Lecture notes delivered in Barcellona in the fall of 2003

Introduction to superfluidity -- Field-theoretical approach and applications: https://arxiv.org/abs/1404.1284

Andreas Schmitt

In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also discuss various applications in low-energy and high-energy physics. Besides some introductory and standard topics such as superfluid helium and superfluidity in a simple scalar field theory, the lecture notes also include more advanced chapters, for instance discussions of the covariant two-fluid formalism and Cooper pairing with mismatched Fermi surfaces.

Comments: 150 pages, v2: minor corrections, typos fixed, references added, version published in Lect. Notes Phys. 888, 1-155 (2014), ISBN 978-3-319-07946-2

Boson-Fermion Model of High-T_C Superconductivity ----A Progress Report: https://arxiv.org/abs/cond-mat/9811230

Hai-cang Ren

This is an invited lecture at the XXII International School of Theoretical Physics, Ustron, Poland, 9/10-9/15, 1998. The boson-fermion model of high T_C superconductivity is reviewed. Its applications to the pseudo-gap and DC transport coefficients are discussed.

Comments: 14 pages, 3 figures; A few changes in the quotations

Effective Gauge Theories, The Renormalization Group, and High-Temperature Superconductivity: https://arxiv.org/abs/cond-mat/9810324

A. Campbell-Smith, N.E. Mavromatos

These lectures serve as an introduction to the renormalization group approach to effective field theories, with emphasis on systems with a Fermi surface. For such systems, demanding appropriate scaling with respect to the renormalization group for the appropriate excitations leads directly to the important concept of quasiparticles and the connexion between large-N_f treatments and renormalization group running in theory space. In such treatments N_f denotes the number of effective fermionic degrees of freedom above the Fermi surface; this number is roughly proportional to the size of the Fermi surface. As an application of these ideas, non-trivial infra red structure in three dimensional U(1) gauge theory is discussed, along with applications to the normal phase physics of high-T_c superconductors, in an attempt to explain the experimentally observed deviations from Fermi liquid behaviour. Specifically, the direct current resistivity of the theory is computed at finite temperatures, T, and is found to acquire O(1/Nf) corrections to the linear T behaviour. Such scaling corrections are consistent with recent experimental observations in high T_c superconducting cuprates.

Comments: 38 pages LATEX, figures incorporated (incorrect citation ref. [3] corrected; no other changes)

Renormalization Group Methods: Landau-Fermi Liquid and BCS Superconductor: https://arxiv.org/abs/cond-mat/9508063

J. Froehlich, T. Chen, M. Seifert

This is the second part of the notes to the course on quantum theory of large systems of non-relativistic matter taught by J. Fröhlich at the 1994 Les Houches summer school. It is devoted to a sketchy exposition of some of the beautiful and important, recent results of J.Feldman and E.Trubowitz, and J. Feldman, H. Knörrer, D. Lehmann, J. Magnen, V. Rivasseau and E. Trubowitz. Their results are about a mathematical analysis of non-relativistic many-body theory, in particular of the Landau-Fermi liquid and BCS superconductivity, using Wilson's renormalization group methods and the techniques of the 1/N-expansion. While their work is ultimately aimed at a complete mathematical control (beyond perturbative expansions) of systems of weakly coupled electron gases at positive density and small or zero temperature, we can only illustrate some of their ideas within the context of perturbative solutions of Wilson-type renormalization group flow equations (we calculate leading-order terms in a 1/N-expansion, where N is an energy scale) and of one-loop effective potential calculations of the BCS superconducting ground state. Contents:

1. Background material

2. Weakly coupled electron gases

3. The renormalization group flow

4. Spontaneous breaking of gauge invariance, and superconductivity

Comments: 50 pages, Latex2e. Part II of lectures presented by J.F. at the 1994 Les Houches Summer School ``Fluctuating Geometries in Statistical Mechanics and Field Theory'' (also available at this http URL ). For part I, see cond-mat/9508062

Quantum Theory of Large Systems of Non-Relativistic Matter: https://arxiv.org/abs/cond-mat/9508062

J. Froehlich, U.M. Studer, E. Thiran

1. Introduction

2. The Pauli Equation and its Symmetries {2.1} Gauge-Invariant Form of the Pauli Equation {2.2} Aharonov-Bohm Effect {2.3} Aharonov-Casher Effect

3. Gauge Invariance in Non-Relativistic Quantum Many-Particle Systems {3.1} Differential Geometry of the Background {3.2} Systems of Spinning Particles Coupled to External Electromagnetic and Geometric Fields {3.3} Moving Coordinates and Quantum-Mechanical Larmor Theorem

4. Some Key Effects Related to the U(1)×SU(2) Gauge Invariance of Non-Relativistic Quantum Mechanics {4.1} ``Tidal'' Aharonov-Bohm and ``Geometric'' Aharonov-Casher Effects {4.2} Flux Quantization {4.3} Barnett and Einstein-deHaas Effects {4.4} Meissner-Ochsenfeld Effect and London Theory of Superconductivity {4.5} Quantum Hall Effect

5. Scaling Limit of the Effective Action of Fermi Systems, and Classification of States of Non-Relativistic Matter

6. Scaling Limit of the Effective Action of a Two-Dimensional, Incompressible Quantum Fluid {6.1} Scaling Limit of the Effective Action {6.2} Linear Response Theory and Current Sum Rules {6.3} Quasi-Particle Excitations and a Spin-Singlet Electron Pairing Mechanism

7. Anomaly Cancellation and Algebras of Chiral Edge Currents in Two- Dimensional, Incompressible Quantum Fluids {7.1} Integer Quantum Hall Effect and Edge Currents {7.2} Edge Excitations in Spin-Polarized Quantum Hall Fluids

8. Classification of Incompressible Quantum Hall Fluids {8.1} QH Fluids and QH Lattices: Basic Concepts {8.2} A Dictionary Between the Physics of QH Fluids and the Mathematics of QH Lattices {8.3} Basic Invariants of Chiral QH Lattices (CQHLs) and their Physical Interpretations {8.4} General Theorems and Classification Results for CQHLs {8.5} Maximally Symmetric CQHLs {8.6} Summary and Physical Implications of the Classification Results

Comments: 145 pages, Latex2e. Part I of lectures presented by J.F. at the 1994 Les Houches Summer School ``Fluctuating Geometries in Statistical Mechanics and Field Theory'' (also available at this http URL ). For part II, see cond-mat/9508063