Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals

We investigate the usefulness of the ''string-inspired technique'' for gauge theory calculations in a constant external field background. Our approach is based on Strassler's worldline path integral approach to the Bern-Kosower formalism, and on the construction of worldline (super-) Green's functions incorporating external fields as well as internal propagators. The worldline path integral representation of the gluon loop is reexamined in detail. We calculate the two-loop effective actions induced for a constant external field by a scalar and spinor loop, and the corresponding one-loop effective action in the gluon loop case. (C) 1997 Academic Press.