Classical scalar and spinning particles interacting with external Yang-Mills fields

Abstract

We derive the classical equations of motion for scalar and spinning particles interacting with an external Yang-Mills field. The internal degrees of freedom are described by a set of Grassmann variables; in this way, after quantization, we get automatically finite-dimensional representations of the internal symmetry group. By requiring that the Lagrangian is gauge invariant we determine the general form for the coupling terms. In particular we obtain a generalized version of the Bargmann-Michel-Telegdi equation, which is valid for a spin- 1 2 particle in an arbitrary external field.