  A systematic derivation is given of the worldline path integrals for the
effective action of a multiplet of Dirac fermions interacting with general
matrix-valued classical background scalar, pseudoscalar, and vector gauge
fields. The first path integral involves worldline fermions with antiperiodic
boundary conditions on the worldline loop and generates the real part of the
one loop (Euclidean) effective action. The second path integral involves
worldline fermions with periodic boundary conditions and generates the
imaginary part of the (Euclidean) effective action, i.e. the phase of the
fermion functional determinant. Here we also introduce a new regularization for
the phase of functional determinants resembling a heat-kernel regularization.
Compared to the known special cases, our worldline Lagrangians have a number of
new interaction terms; the validity of some of these terms is checked in
perturbation theory. In particular, we obtain the leading order contribution
(in the heavy mass expansion) to the Wess-Zumino-Witten term, which generates
the chiral anomaly.
