Galilean invariance is a desired property for classical non-relativistic theories. Guiding center theory describes the slow drift motion of charged particles in strong magnetic fields. While one can guarantee a Hamiltonian formulation to all orders, it was previously unknown whether such a theory can possess Galilean symmetry. We show that specific first- and second-order guiding center models are Galilean invariant. Furthermore, we prove that one can ensure Galilean invariance to all orders.
Stephens et al. (Wed,) studied this question.