Infinite-Component Local Field Theory with a Rising Mass Spectrum

An infinite-component field theory is proposed to describe the $\rho$ Regge family of particles. Using the generators of the group $O(3, 2)$, a class of first-order wave equations is obtained. The simplest of this class of equations is solved to yield a rising mass spectrum with a hydrogenlike accumulation point. Because only finite-dimensional representations of the homogeneous Lorentz group appear in the theory, it is free from many of the difficulties, including noncausality, which have plagued other infinite-component field theories with nontrivial mass spectra.