On Galilean Covariance in a Nonrelativistic Model Involving a Chern–Simons Term

Abstract

We consider a nonrelativistic model where a Schrodinger field has been coupled to an abelian Chern–Simons term. By performing Hamiltonian analysis of the model using the Faddeev–Jackiw symplectic method, we first demonstrate the closure of the Galilean algebra at the classical level in a gauge independent manner. By suitably taking into account the effects of operator ordering, we then show once again in a gauge independent way that this closure is also preserved for the corresponding quantum theory. The gauge fixed analysis, on the contrary, reveals that galilean invariance is valid only for the classical case. This is explicitly demonstrated both for the radiation gauge, as well as for a nonconventional gauge where the phase of the scalar field is fixed. Subtleties related to the definition of the angular momentum operator, both at the classical and quantum levels, are illuminated.