# Gauge invariance and current algebra in nonrelativistic many body theory

@article{Frhlich1993GaugeIA, title={Gauge invariance and current algebra in nonrelativistic many body theory}, author={J{\"u}rg Fr{\"o}hlich and Urban M. Studer}, journal={Reviews of Modern Physics}, year={1993}, volume={65}, pages={733-802} }

The main purpose of this paper is to further our theoretical understanding of the fractional quantum Hall effect, in particular of spin effects, in two-dimensional incompressible electron fluids subject to a strong, transverse magnetic field. As a prerequisite for an analysis of the quantum Hall effect, the authors develop a general formulation of the many-body theory of spinning particles coupled to external electromagnetic fields and moving through a general, geometrically nontrivial…

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## References

SHOWING 1-10 OF 147 REFERENCES

U(1)×SU(2)-gauge invariance of non-relativistic quantum mechanics, and generalized Hall effects

- Physics
- 1992

We show that the non-relativistic quantum mechanics of particles with spin coupled to an electromagnetic field has a naturalU(1)×SU(2) gauge invariance. Ward identities reflecting this gauge…

Topologically Massive Gauge Theories

- Physics
- 1982

Gauge vector and gravity models are studied in three-dimensional space-time, where novel, gauge invariant, P and T odd terms of topological origin give rise to masses for the gauge fields. In the…

Spin Singlet Quantum Hall Effect and Nonabelian Landau-Ginzburg Theory

- Physics
- 1991

In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged…

Braid statistics in local quantum theory

- Mathematics
- 1990

We present details of a mathematical theory of superselection sectors and their statistics in local quantum theory over (two- and) three-dimensional space-time. The framework for our analysis is…

Boundary conditions for quantum mechanics on cones and fields around cosmic strings

- Physics
- 1991

We study the options for boundary conditions at the conical singularity for quantum mechanics on a two-dimensional cone with deficit angle ≦ 2π and for classical and quantum scalar fields propagating…

Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field

- Physics
- 1959

The problem of the precession of the “spin” of a particle moving in a homogeneous electromagnetic field — a problem which has recently acquired considerable experimental interest — has already been…

Spin-statistics theorem and scattering in planar quantum field theories with braid statistics

- Physics, Mathematics
- 1991