Galilean-invariance ambiguity in the nonrelativistic pion-nucleon absorption operator

Abstract

In the model of a nucleon interacting with a massive object via a potential in the Dirac equation, we have demonstrated that the behavior of the nonrelativistic pion absorption operator under Galilean transformations depends upon the properties of the potential under Lorentz transformations. In particular, the operator has a Galilean invariant form if the potential is the time-like component of a four-vector, but not if the potential is a scalar.