# Quantum Theory of Large Systems of Non-Relativistic Matter

@article{Froehlich1994QuantumTO, title={Quantum Theory of Large Systems of Non-Relativistic Matter}, author={Juerg Froehlich and Urban M. Studer and Emmanuel Thiran}, journal={arXiv: Condensed Matter}, year={1994} }

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 $U(1) \times SU(2)$ Gauge…

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#### References

SHOWING 1-10 OF 12 REFERENCES

The Fractional Quantum Hall Effect: Properties of an Incompressible Quantum Fluid

- Physics
- 1988

1. Introduction.- 2. Ground State.- 2.1 Finite-Size Studies: Rectangular Geometry.- 2.2 Laughlin's Theory.- 2.3 Spherical Geometry.- 2.4 Monte Carlo Results.- 2.5 Reversed Spins in the Ground State.-…

The effective gauge field action of a system of non-relativistic electrons

- Physics
- 1995

We consider a system of free, non-relativistic electrons at zero temperature and positive density, coupled to an arbitrary, external electromagnetic vector potential,A. By integrating out the…

From phase transitions to chaos : topics in modern statistical physics

- Physics
- 1992

Anisotropic segregation in a gravitational field, K. Binder et al replica symmetry breaking in the ising spin glass in finite dimensions, C. De Dominicis and I. Kondor problems of high-Tc…

Topological BF theories in 3 and 4 dimensions

- Mathematics, Physics
- 1995

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2‐knots (in 4 dimensions). The vacuum…

Quantum Many-Particle Systems

- Physics
- 1988

* Second Quantization and Coherent States * General Formalism at Finite Temperature * Perturbation Theory at Zero Temperature * Order Parameters and Broken Symmetry * Greens Functions * The Landay…

Field theories of condensed matter systems

- Physics
- 1991

ForewordIntroductionThe Hubbard ModelThe Magnetic Instability of the Fermi SystemOne-Dimensional Quantum AntiferromagnetsSigma Models, Topological Terms and Spin LiquidsThe Spin Liquid StatesChiral…

Current Algebra and Anomalies

- Computer Science
- 1985

This collection of surveys on current algebra and anomalies is a successor volume to Lectures on Current Algebra and Its Applications (Princeton Series in Physics, 1972), originally published in 1986.

Superconductivity Of Metals And Alloys

- Physics
- 1966

Drawn from the author's introductory course at the University of Orsay, Superconductivity of Metals and Alloys is intended to explain the basic knowledge of superconductivity for both…

Electrodynamics of continuous media

- Physics, Materials Science
- 1960

Electrostatics of conductors Static magnetic field Superconductivity The propagation of electromagnetic waves Spatial dispersion Diffraction of X rays in crystals.