UNKNOTTING THE POLARIZED VACUUM OF QUENCHED QED

A knot-theoretic explanation is given for the rationality of the quenc hed QED beta function. At the link level, the Ward identity entails ca ncellation of subdivergences generated by one term of the skein relati on, which in turn implies cancellation of knots generated by the other term. In consequence, each bare three-loop diagram has a rational Lau rent expansion in the Landau gauge, as is verified by explicit computa tion. Comparable simplification is found to occur in scalar electrodyn amics, when computed in the Duffin-Kemmer-Petiau formalism.