The Wave Equation for Spin 1 in Hamiltonian Form. II
Abstract
The investigation is mainly concerned with the relation between constants of the motion and the conservation laws in differential form. The operator that commutes with the Hamiltonian is not the one whose Hermitian form obeys a conservation law and therefore yields, on integration over space, the mean (or expectation) value of the constant. There is a general association between the 'commuting' and the 'conserved' operators; the latter does not in general commute with the Hamiltonian. The duplication stems from normalizing by a nondefinite Hermitic form, meaning the charge density. It entails that an elementary wave always carries a positive amount of energy, and a momentum in the direction in which the wave proceeds, though from the eigenvalues of energy and momentum one might expect either sign. A deeprooted general connexion between charge quantization and the energy aspect of frequency is suggested. An attempt is made to clarify the relation between mechanical and magnetic spin, the latter appearing to depend in a simple way on the fifth Kemmer matrix.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 November 1955
 DOI:
 10.1098/rspa.1955.0229
 Bibcode:
 1955RSPSA.232..435S