SEMISCALAR REPRESENTATIONS OF THE LORENTZ GROUP AND PROPAGATION EQUATIONS

We construct semiscalar linear representations of the inhomogeneous Lo rentz group by considering the invariance of linear propagation equati ons. There is only one semiscalar representation, and the most general linear propagation equation that admits this Lorentz representation i s a telegrapher/Maxwell-Cattaneo type equation, whose elementary solut ions propagate at the speed of light. Under a Lorentz boost along the x(1) axis, the propagated field variable transforms as U' = U exp q[y( v)(vx(1) - c(2)t) + c(2)t]. If one imposes U' = U, then the Lorentz bo ost of the propagation equation acquires a velocity-dependent convecti on-type term. in the Newtonian limit c --> infinity, the equation redu ces to the Fourier heat equation, and previous results on semiscalar r epresentations of the Galilean group are regained.