First quantized pair interactions

The parametrized Dirac wave equation for multiple particles is shown here to yield the standard cross sections for creation and annihilation of fermion pairs, while avoiding the paradoxes arising from the standard single-particle Dirac equation and hole theory. These paradoxes were originally overcome with Quantum Field Theory. The creation and annihilation operators of Quantum Field Theory are subject to causality conditions which preclude entanglement across distances greater than the order of the Compton wavelength. The parametrized first-quantized formalism requires no causality condition for fermions, and it admits fermion entanglement across all of space and time, while ensuring covariant Dyson series and ${\mathcal TPC}$ invariance.