The wave equation for spin 1 in Hamiltonian form

Abstract

If from the differential equations that hold in a Proca field you select the ten that express the time derivatives of the ten components involved, i. e. of the ‘electromagnetic’ field and its potential vector, you obtain right away for the ten-componental entity an equation that may be said to be at the same time of the Schrödinger, the Dirac and the Kemmer type. The four 10 x 10-matrices that occur as coefficients are Hermitian and satisfy Kemmer’s commutation rules. The fifth is easily constructed. Those of the Proca equations that were not included are merely injunctions on the initial value. They are expressed by one matrix equation, that makes it evident that, once posited, they are preserved. The three spin matrices are indicated. The spin number is 1 or 0, but the aforesaid injunctions exclude 0.