The AngleGeometry of Spacetime and Classical Charged Particle Motion
Abstract
The fivedimensional angle metric of spacetime is defined, and its connection with the conformal (anglepreserving) group C of transformations of spacetime explained. This is an application to physics of the "sphere geometry" developed in the last century by Liouville, F. Klein, Möbius et al. The extra degree of freedom λ plays several observable roles in solutions of the field equations of the theory (which are uniquely fixed by Cinvariance and gaugeinvariance under the assumed internal symmetries). In the solution for a gauge boson with arbitrarily moving point source, λ appears as a microscopic "parameter" which enforces a nonzero minimum time lag in causal signal propagation. We show how this enables a nonsingular selfinteraction to be defined in classical particle motion having the correct properties. There is the correct radiationreaction term, but unphysical features of the fourdimensional theory: third order motion equations, runaway solutions, infinite "electromagnetic" mass, etc. are avoided. In free field wave function solutions λ is seen to be conjugate to mass (just as r is to p and t is to E) and provides a mass operator.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 1998
 DOI:
 10.1142/S0218271898000413
 Bibcode:
 1998IJMPD...7..603I