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The spin-statistics connection has been proved for nonrelativistic quantum mechanics (Jabs, A., 2010: Found. Phys., 40, 776-792). The proof is extended here to the relativistic regime using the parametrized Dirac equation. A causality condition is not required. * afbennett97333@post.harvard.edu 2

The parametrized Duffin-Kemmer-Petiau wave equation is formulated here for many relativistic particles of spin-0 or spin-1. The conventional second-quantized or Fock-space proof of the spin-statistics connection requires that the fields of creation and annihilation operators satisfy commutation relations subject to causality conditions. The conditions restrict entanglement to spacelike separations of the order of the Compton wavelength /mc. Relativistic quantum mechanics is used here to prove the symmetry of the wavefunctions for identical particles, following the nonrelativistic argument of Jabs (Found. Phys. 2010, 40, 776-792). First quantization does not require causal commutation relations, and so entanglement is unrestricted.

The parametrized relativistic quantum mechanics of Stueckelberg [Helv. Phys. Acta 15, 23 (1942)] represents time as an operator, and has been shown elsewhere to yield the recently observed phenomena of quantum interference in time, quantum diffraction in time and quantum entanglement in time. The Stueckelberg wave equation as extended to a spin-1/2 particle by Horwitz and Arshansky [J. Phys. A: Math. Gen. 15, L659 (1982)] is shown here to yield the electron g-factor g = 2 (1 + α/2π), to leading order in the renormalized fine structure constant α, in agreement with the quantum electrodynamics of Schwinger [Phys. Rev., 73, 416L (1948)].

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