THE ANGLE-GEOMETRY OF SPACETIME AND CLASSICAL CHARGED-PARTICLE MOTION

The five-dimensional angle metric of spacetime is defined, and its con nection with the conformal (angle-preserving) group C of transformatio ns of spacetime explained. This is an application to physics of the '' sphere geometry'' developed in the last century by Liouville, F. Klein , Mobius et al. The extra degree of freedom lambda plays several obser vable roles in solutions of the field equations of the theory (which a re uniquely fixed by C-invariance and gauge-invariance under the assum ed internal symmetries). In the solution for a gauge boson with arbitr arily moving point source, lambda appears as a microscopic ''parameter '' which enforces a nonzero minimum time lag in causal signal propagat ion. We show how this enables a nonsingular self-interaction to be def ined in classical particle motion having the correct properties. There is the correct radiation-reaction term, but unphysical features of th e four-dimensional theory: third order motion equations, runaway solut ions, infinite ''electromagnetic'' mass, etc, are avoided. In free fie ld wave function solutions lambda is seen to be conjugate to mass (jus t as r is to p and t is to E) and provides a mass operator.