Relativistic Wave Equations for Particles with Internal Structure and Mass Spectrum

Abstract

Relativistic wave equations may be expected to play two roles, which we will call kinematical and dynamical. In the kinematical sense, a wave equation singles out a particle of definite mass and spin, usually together with its anti-particle counterpart, and specifies how the components of the wave function transform as we change its state of motion or our reference system. This law of transformation must be in accordance with the Poincare group,**) and therefore a wave equation should characterize an irreducible unitary representation of that group appropriate to quantum mechanical description of a particle!) In the dynamical sense, however, a wave equation ought to serve more purposes. It should be able to describe not only an isolated free particle, but also a particle in interaction, at least with classical fields such as the electromagnetic and gravitational fields, and ideally with all other dynamical fields and associated particles. A wave equation then becomes an equation