  This is the second paper in a series on the dynamics of matter fields in the
causal set approach to quantum gravity. We start with the usual expression for
the Lagrangian of a charged scalar field coupled to a SU(n) Yang-Mills field,
in which the gauge field is represented by a connection form, and show how to
write it in terms of holonomies between pairs of points, causal relations, and
volumes or timelike distances, all of which have a natural correspondence in
the causal set context. In the second part of the paper we present an
alternative model, in which the gauge field appears as the result of a
procedure inspired by the Kaluza-Klein reduction in continuum field theory, and
the dynamics can be derived simply using the gravitational Lagrangian of the
theory.
