Chirality and parity in a first-quantized representation

We study the realization of chiral and parity transformations within a particle-like path-integral representation for Dirac fields, showing how those transformations can be implemented in a natural way within the formalism. We then obtain a representation for the chiral fermion propagator and determinant within this framework, and also formulate a way to define the average of the propagator over a random mass in $d=2n$ dimensions.