Inverse Mass Expansions from Worldline Path Integrals - Higher Order Coefficients and Ordering Problems

Higher order coefficients of the inverse mass expansion of one--loop effective actions are obtained from a one--dimensional path integral representation. For the evaluation of the path integral with Wick contractions a suitable Green function has to be chosen. We consider the case of a massive scalar loop in the background of both a scalar potential and a (non--abelian) gauge field. For the pure scalar case the method yields the coefficients of the expansion in a minimal set of basis terms whereas complicated ordering problems arise in gauge theory. An appropriate reduction scheme is discussed.