Schrödinger Fields on the Plane with $[U(1){]}^N$ Chern-Simons Interactions and Generalized Self-dual Solitons

Abstract

A general non-relativistic field theory on the plane with couplings to an arbitrary number of abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We identify the self-dual systems for which certain classical and quantal aspects of the theory can be studied in a much simplified mathematical setting. Then, specializing to the general self-dual system with two Chern-Simons gauge fields (and non-vanishing mutual statistics parameter), we present a systematic analysis for the static vortexlike classical solutions, with or without uniform background magnetic field. Relativistic generalizations are also discussed briefly.

49 pages including 4 figures, LATEX ( three LATEX figures and one PICTEX figure), SNUTP 93-14, UMN-TH-1135

References in corpus (4)

• Semilocal strings and monopoles
• Chern-Simons Solitons, Toda Theories and the Chiral Model
• Self-dual Vortices in the Generalized Abelian Higgs Model with Independent Chern-Simons Interaction
• Mutual statistics, braid group, and the fractional quantum Hall effect

Cited by in corpus (25)

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• Spontaneously broken abelian Chern-Simons theories
• Schrödinger Fields on the Plane with non-Abelian Chern-Simons Interactions
• Uniqueness of topological multi-vortex solutions for a skew-symmetric Chern-Simons system
• The domain geometry and the bubbling phenomenon of rank two Gauge theory
• Semilocal Self-Dual Chern-Simons Solitons and Toda-type Eqations
• Effect of rotation symmetry to abelian Chern-Simons field theory and anyon equation on a sphere
• Only hybrid anyons can exist in broken symmetry phase of nonrelativistic $U(1{)}^2$ Chern-Simons theory
• Abelian Chern-Simons field theory and anyon equation on a torus
• Operator Ordering Problem of the Nonrelativistic Chern-Simons Theory
• Structure of bubbling solutions of Liouville systems with negative singular sources
• Semiclassical Theory for Two-anyon System
• Some exact solutions of the semilocal Popov equations
• BPS Vortices, $Q$-balls, and $Q$-vortices in $\mathcal{N}=6$} Chern-Simons Matter Theory
• The Energy Density in the Maxwell-Chern-Simons Theory
• Self-dual Maxwell-Chern-Simons solitons in a parity-invariant scenario
• On Liouville systems at critical parameters, Part 2: Multiple bubbles
• Some Exact Solutions of the Semilocal Popov Equations with Many Flavors
• New Gauge Invariant Formulation of the Chern-Simons Gauge Theory: Classical and Quantal Analysis
• Construction of Multi-Bubble Solutions for a System of Elliptic Equations arising in Rank Two Gauge Theory
• Vortices in a parity-invariant Maxwell-Chern-Simons model
• Existence results for a non-relativistic Chern-Simons model with purely mutual interaction