  We discuss the discrete symmetries of the Stueckelberg-Schrodinger
relativistic quantum theory and its associated 5D local gauge theory, a
dynamical description of particle/antiparticle interactions, with monotonically
increasing Poincare-invariant parameter. In this framework, worldlines are
traced out through the parameterized evolution of spacetime events, advancing
or retreating with respect to the laboratory clock, with negative energy
trajectories appearing as antiparticles when the observer describes the
evolution using the laboratory clock. The associated gauge theory describes
local interactions between events (correlated by the invariant parameter)
mediated by five off-shell gauge fields. These gauge fields are shown to
transform tensorially under under space and time reflections, unlike the
standard Maxwell fields, and the interacting quantum theory therefore remains
manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory
is achieved by simultaneous reflection of the sense of evolution and the fifth
scalar field. Applying this procedure to the classical gauge theory leads to a
purely classical manifestation of charge conjugation, placing the CPT
symmetries on the same footing in the classical and quantum domains. In the
resulting picture, interactions do not distinguish between particle and
antiparticle trajectories -- charge conjugation merely describes the
interpretation of observed negative energy trajectories according to the
laboratory clock.
