Spinor electrodynamics as a dynamics of currents

Abstract

Spinor electrodynamics, consisting of the minimally coupled Dirac and Maxwell equations, is shown to be equivalent to sixteen equations for sixteen currents ${J}^{0}$, ${J}^{a}$, ${L}^{[\mathrm{ab}]}$, ${K}^{a}$, ${K}^{0}$, consisting of one scalar bilinear identity, a vector set of four quintic differential equations of third order, a skew tensor set of six cubic identities, an axial-vector set of four bilinear compatibility relations of first order, and one pseudoscalar bilinear identity. The conservation of the vector current ${J}^{a}$ follows from the vector set of equations, and the partial conservation of the axial-vector current ${K}^{a}$ follows from the remaining twelve equations. There is an additional independent constraining scalar bilinear identity which ensures that these twelve equations are consistent with conservation of the vector current.