An infinite-component particle equation with a widely spaced mass spectrum

Abstract

Infinite-component wave equations have been studied by several authors for the generation of mass eigenvalues, that might explain the masses of the elementary particles. So far no spectra have been found with any resemblance to the existing masses, the intervals rising far too slowly or even descending. We employ here a wave equation based on a unitary representation of the Lorentz transformation with nonvanishing Casimir operators (I andK), one of which (K) is continuous. With its help mass operators are easily formulated and analysed. We evaluate a particularly simple one constructed earlier in an attempt to quantize the motion of electrically charged particles under the influence of their own field. There results a well-defined discrete and increasing, but too widely spaced mass spectrum. The largeness of the intervals is caused by the smallness of the electromagnetic coupling constant(e2/ℏc) that enters by its reciprocal value. Hence a field with a larger coupling effect, perhaps Heisenberg's matter field, should modify the distribution in the right sense.