Spin 1/2 and Invariant Coefficients

TL;DR

This paper extends spinor field theory to include translation symmetry by developing 8-spinors, revealing that four components behave like standard Dirac spinors while the other four relate to electromagnetic potentials, uniting matter and gauge fields.

Contribution

It introduces an 8-spinor framework incorporating translation symmetry, linking conventional Dirac spinors with electromagnetic potentials within a unified field theory.

Findings

Four components satisfy the Dirac equation.

Remaining four components relate to electromagnetic potentials.

The 8-spinor current is proportional to the electromagnetic 4-vector potential.

Abstract

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.