Galilean Symmetry in a Nonabelian Chern–Simons Matter System

Abstract

We study the Galilean symmetry in a nonrelativistic model involving the coupling of a nonabelian Chern–Simons term with matter fields. The validity of the classical Galilean algebra on the constraint surface is demonstrated in the gauge independent formalism. An identical conclusion also holds for the quantum analysis by properly accounting for the ordering effects. The classical reduced space formulation is then discussed in the axial gauge using both the symplectic and Dirac methods. Conditions on the Green functions are necessary to preserve the equivalence among these methods. Interestingly, these conditions are once again required to demonstrate the validity of either the classical or quantum Galilean algebra in the reduced space formulation.