We further develop the new approach, proposed in part I (hep-th/9807072), to
computing the heat kernel associated with a Fermion coupled to vector and axial
vector fields. We first use the path integral representation obtained for the
heat kernel trace in a vector-axialvector background to derive a Bern-Kosower
type master formula for the one-loop amplitude with M vectors and N
axialvectors, valid in any even spacetime dimension. For the massless case we
then generalize this approach to the full off-diagonal heat kernel. In the D=4
case the SO(4) structure of the theory can be broken down to SU(2)ΓSU(2) by use of the 't Hooft symbols. Various techniques for explicitly
evaluating the spin part of the path integral are developed and compared. We
also extend the method to external fermions, and to the inclusion of isospin.
On the field theory side, we obtain an extension of the second order formalism
for fermion QED to an abelian vector-axialvector theory.Comment: Sequel to hep-th/9807072, references added, some clarifications and
corrections, 29 pages, RevTex, 8 diagrams using epsfig.st