Abstract
We study the propagator of a colored scalar particle in the background of a non-abelian gauge field using the worldline formalism. It is obtained by considering the open worldline of a scalar particle with extra degrees of freedom needed to take into account the color charge of the particle, which we choose to be in the fundamental representation of the gauge group. Specializing the external gauge field to be given by a sum of plane waves, i.e. a sum of external gluons, we produce a master formula for the scalar propagator with an arbitrary number of gluons directly attached to the scalar line, akin to similar formulas derived in the literature for the case of the scalar particle performing a loop. Our worldline description produces at the same time the situation in which the particle has a color charge given by an arbitrarily chosen symmetric or antisymmetric tensor product of the fundamental.
Highlights
We study the propagator of a colored scalar particle in the background of a non-Abelian gauge field using the worldline formalism
Specializing the external gauge field to be given by a sum of plane waves, i.e. a sum of external gluons, we produce a master formula for the scalar propagator with an arbitrary number of gluons directly attached to the scalar line, akin to similar formulas derived in the literature for the case of the scalar particle performing a loop
The worldline representation of effective actions has seen a great deal of activity in the past twenty years, starting with the work of Strassler [1], who rederived the BernKosower master formulas [2,3] directly from point particle path integrals; see Ref. [4] for a review
Summary
The worldline representation of effective actions has seen a great deal of activity in the past twenty years, starting with the work of Strassler [1], who rederived the BernKosower master formulas [2,3] directly from point particle path integrals; see Ref. [4] for a review. One possibility is to couple them to a worldline U(1) gauge field, which allows for a Chern-Simons term whose coupling constant is chosen to project onto the desired irrep This is the method already seen at work in the worldline description of p-forms [12,42], later extended to the treatment of color charges. We show how to employ commuting auxiliary variables with a Chern-Simons term to study the propagator of a scalar particle in the background of a non-Abelian gauge field by representing it as a suitable worldline path integral. One may specialize the external gauge field to be given by a sum of plane waves (external gluons) and perform the path integral This produces a master formula generating the propagator with an arbitrary number of gluons directly attached to it. The choice is again made by selecting an appropriate Chern-Simons coupling
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