The construction of gauge-links in arbitrary hard processes

Transverse momentum dependent parton distribution and fragmentation functions are described by hadronic matrix elements of bilocal products of field operators off the light-cone. These bilocal products contain gauge-links, as required by gauge-invariance. The gauge-links are path-ordered exponentials connecting the field operators along a certain integration path. This integration path is process-dependent, depending specifically on the short-distance partonic subprocess. In this paper we present the technical details needed in the calculation of the gauge-links, and a calculational scheme is provided to obtain the gauge invariant distribution and fragmentation correlators corresponding to a given partonic subprocess.