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We use the worldline path-integral approach to the Bern-Kosower formalism fordeveloping a new algorithm for calculation of the sum of all diagrams with onespinor loop and fixed numbers of external and internal photons. The method isbased on worldline supersymmetry, and on the construction of generalizedworldline Green functions. The two-loop QED $\beta$ -- function is calculatedas an example.Comment: uuencoded ps-file, 20 pages, 2 figures, final revised version to  appear in Phys. Rev.

Multiloop calculations in the string-inspired formalism: The single spinor loop in QED