  Relativistic particle actions are a useful tool to describe quantum field
theory effective actions using a string-inspired first-quantized approach. Here
we describe how to employ suitable particle actions in the computation of the
scalar contribution to the one-loop gluon effective action. We use the
well-known method of introducing auxiliary variables that create the color
degrees of freedom. In a path integral they implement automatically the path
ordering needed to ensure gauge invariance. It is known that the color degrees
of freedom introduced this way form a reducible representation of the gauge
group. We describe a method of projecting onto the fundamental representation
(or any other chosen irrep, if desired) of the gauge group. Previously, we have
discussed the case of anticommuting auxiliary variables. Choosing them to be in
the fundamental representation allows to obtain, without any extra effort, also
the situation in which the color is given by any antisymmetric tensor product
of the fundamental. Here, we describe the novel case of bosonic auxiliary
variables. They can be used equivalently for creating the color charges in the
fundamental representation. In addition one gets, as a byproduct, the cases
where the particle can have the color sitting in any symmetric tensor product
of the fundamental. This is obtained by tuning to a different value a Chern
Simons coupling, present in the model, which controls how the projection is
achieved.
