Pair production in classical Stueckelberg-Horwitz-Piron electrodynamics

In this paper we calculate pair production from bremsstrahlung as a classical effect in Stueckelberg-Horwitz-Piron electrodynamics. In this framework, worldlines are traced out dynamically through the evolution of events $x^{\mu }(\tau )$ parameterized by a chronological time $\tau$ that is independent of the spacetime coordinates. These events, defined in an unconstrained 8D phase space, interact through five $\tau$-dependent gauge fields induced by the event evolution. The resulting theory differs in its underlying mechanics from conventional electromagnetism, but coincides with Maxwell theory in an equilibrium limit. In particular, the total mass-energy-momentum of particles and fields is conserved, but the mass-shell constraint is lifted from individual interacting events, so that the standard Feynman-Stueckelberg interpretation of pair creation/annihilation is implemented in classical mechanics.