The structure of linear relativistic wave equations. I

Abstract

The structure of linear relativistic wave equations of the form ( iα µ ∂ µ - X ) ψ = 0 is discussed. In general, such equations describe particles with a spectrum of mass and spin values. It is proved that the physical requirement that all particle states can be unambiguously specified by the momentum, mass, spin and charge, leads to a complete determination of the eigenvalues of the total spin. These must form an arithmetical progression S H , S H — 1, S H — 2, ..., terminating at 0, 1/2 or 1. A coupling diagram is associated with every wave equation and necessary restrictions on the shape of the diagram are worked out. There results a useful reduction in the number of mathematical possibilities.