  The N=2 spinning particle action describes the propagation of antisymmetric
tensor fields, including vector fields as a special case. In this paper we
study the path integral quantization on a one-dimensional torus of the N=2
spinning particle coupled to spacetime gravity. The action has a local N=2
worldline supersymmetry with a gauged U(1) symmetry that includes a
Chern-Simons coupling. Its quantization on the torus produces the one-loop
effective action for a single antisymmetric tensor. We use this worldline
representation to calculate the first few Seeley-DeWitt coefficients for
antisymmetric tensor fields of arbitrary rank in arbitrary dimensions. As side
results we obtain the correct trace anomaly of a spin 1 particle in four
dimensions as well as exact duality relations between differential form gauge
fields. This approach yields a drastic simplification over standard heat-kernel
methods. It contains on top of the usual proper time a new modular parameter
implementing the reduction to a single tensor field. Worldline methods are
generically simpler and more efficient in perturbative computations then
standard QFT Feynman rules. This is particularly evident when the coupling to
gravity is considered.
