Galilean symmetry in a nonabelian Chern Simons matter system

TL;DR

This paper investigates the Galilean symmetry in a nonrelativistic nonabelian Chern-Simons matter system, demonstrating the algebra's validity, analyzing gauge choices, and addressing anomalies through different formalisms.

Contribution

It provides a detailed analysis of Galilean symmetry in a nonabelian Chern-Simons matter system using gauge-independent, symplectic, and Dirac methods, highlighting conditions to eliminate anomalies.

Findings

Galilean algebra holds on the constraint surface in a gauge-independent formalism.

An anomalous term in the algebra can be removed by specific Green function conditions.

Galilean symmetry is preserved in the Dirac's method approach.

Abstract

We study the Galilean symmetry in a nonrelativistic model, recently advanced by Bak, Jackiw and Pi, involving the coupling of a nonabelian Chern-Simons term with matter fields. The validity of the Galilean algebra on the constraint surface is demonstrated in the gauge independent formalism. Then the reduced space formulation is discussed in the axial gauge using the symplectic method. An anomalous term in the Galilean algebra is obtained which can be eliminated by demanding conditions on the Green function. Finally, the axial gauge is also treated by Dirac's method. Galilean symmetry is preserved in this method. Comparisions with the symplectic approach reveal some interesting features.