Mixed symmetry Wilson-loop interactions in the worldline formalism

Understand

Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group.

• Colour degrees of freedom are carried on the worldline by auxiliary fields, responsible for providing path ordering and the Wilson-loop coupling.
• The Hilbert space of these fields is reducible but we make use of recent work in order to project onto a single, arbitrary, irreducible representation.
• By functionally quantising the resulting theory we show that this procedure correctly generates the Wilson-loop interaction between the gauge field and the matter field taken to transform in a chosen representation.