Worldline path integral for the massive Dirac propagator: A four-dimensional approach

We simplify and generalize an approach proposed by Di Vecchia and Ravndal t o describe a massive Dirac particle in external vector and scaler fields. T wo different path integral representations for the propagator are derived s ystematically without the usual five-dimensional extension and shown to be equivalent due to the supersymmetry of the action. They correspond to a pro jection on the mass of the: particle either continuously or at the end of t he time evolution. It is shown that the supersymmetry transformations are g enerated by shifting and scaling the supertimes and the invariant differenc e of two supertimes is given for the general case. A nonrelativistic reduct ion of the relativistic propagator leads to a three-dimensional path integr al with the usual Pauli Hamiltonian. By integrating out the photons we obta in the effective action for quenched QED and use it to derive the gauge-tra nsformation properties nf the general Green function of the theory. [S1050- 2947(99)04302-4].