Collective Variables of Fermions and Bosonization

Abstract

We first present a general method for extracting collective variables out of non-relativistic fermions by extending the gauge theory of collective coordinates to fermionic systems. We then apply the method to a system of non-interacting flavored fermions confined in a one-dimensional flavor-independent potential. In the limit of a large number of particles we obtain a Lagrangian with the Wess-Zumino-Witten term, which is the well-known Lagrangian describing the non-Abelian bosonization of chiral fermions on a circle. The result is universal and does not depend on the details of the confining potential.

12 pages, plain tex, added new preprint number

References in corpus (5)

• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level
• $W_{\infty }$ coherent states and path-integral derivation of bosonization of non-relativistic fermions in one dimension
• The Electromagnetic Interactions of Electrons in the Lowest Landau Level

Cited by in corpus (25)

• The effective action for edge states in higher dimensional quantum Hall systems
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
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• Quantum Hall effect on $S^3$, edge states and fuzzy $S^3/{\mathbf{Z}}_2$
• Chiral actions from phase space (quantum Hall) droplets
• Kac-Moody theories for colored phase space (quantum Hall) droplets
• Electromagnetic interactions of higher dimensional quantum Hall droplets
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball
• Quantum Hall Effect on the Flag Manifold F_2
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory
• $W_{\infty }$ Algebras, Hawking Radiation and Information Retention by Stringy Black Holes
• Bosonization in higher dimensions via noncommutative field theory
• Bulk and edge excitations of a $\nu =1$ Hall ferromagnet
• Thermofield dynamics and Gravity
• Noncommutative Fluids
• The fermion density operator in the droplet bosonization picture
• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• Exact operator Hamiltonians and interactions in the droplet bosonization method
• Chiral bosons on Bargmann space associated with A${}_r$ Statistics
• Berry Phases in the Bosonization of Nonlinear Edge Modes
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Electromagnetic Excitations of A_n Quantum Hall Droplets
• Bulk and Edge excitations in a $\nu =1$ quantum Hall ferromagnet