2004/06/28 by Richard Shurtleff, Shurtleff, Richard
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.hep-th/0406249
openalex publication_date 2004/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Massive spin 1/2 particles require 2-spinors for rotations, 4-spinors for rotations and boosts with parity. Including translations requires 8-spinors. Adapting 4-spinor field theory to 8-spinor fields with translation symmetry is discussed here. It is shown that four of these spin components act like conventional 4-spinors, satisfying the conventional free-particle Dirac equation. The remaining four components have unconventional coordinate dependence due to translation symmetry. One finds that the 4-vector current of the 8-spinor is proportional to the electromagnetic 4-vector potential of the conventional 4-spinor, with arbitrary charge. Thus translation symmetry in field theory unites a conventional 4-spinor field and its electromagnetic vector potential.