  We derive a geometric representation of couplings between spin degrees of
freedom and gauge fields within the worldline approach to quantum field theory.
We combine the string-inspired methods of the worldline formalism with elements
of the loop-space approach to gauge theory. In particular, we employ the loop
(or area) derivative operator on the space of all holonomies which can
immediately be applied to the worldline representation of the effective action.
This results in a spin factor that associates the information about spin with
"zigzag" motion of the fluctuating field. Concentrating on the case of quantum
electrodynamics in external fields, we obtain a purely geometric representation
of the Pauli term. To one-loop order, we confirm our formalism by rederiving
the Heisenberg-Euler effective action. Furthermore, we give closed-form
worldline representations for the all-loop order effective action to lowest
nontrivial order in a small-N_f expansion.
