Mass spectrum of relativistic invariant equations in an infinite number of dimensions

An analysis is given for the spin dependence of the masses of states described by a relativistically invariant equation in an infinite number of dimensions. It is found that linear equations of GePfand– Yaglom type give rise to branches where the mass increases with the spin, as well as the usual falling branches, if restrictions are applied to the arbitrary element allowed by the relativistic invarianee. It is also found that the falling branches can be suppressed if a certain extension is made in the structure of the linear relativistically invariant equation. Examples are given.