Some considerations about the dynamic of a particle in Stueckelberg - Schroedinger formalism

Some time ago, E. C. G. Stueckelberg has demonstrated [Helv. Phys. Acta 14 (1941) 588, Helv. Phys. Acta 14 (1941) 322, Helv. Phys. Acta 15 (1942) 22, Phys. Rev. 10 (1957) 254] that it is possible to construct a classical and quantum relativistic mechanics theory considering electromagnetic and gravitational interactions if in the Einstein's theory time is considered as a dynamical variable. This theory forgot for many decades, is able to predict the pair particle production as well as the annihilation in classical relativistic mechanics without use of the quantum theory. The motion of an event in space-time is a free universe line. The interaction could bend this world line and then moves on to the possibility that world line can bend so much that it curves back in time. In this theory, an object moving backward in time would appear to have opposite charge if it is thought as having positive energy and therefore is identified as an antiparticle. This interpretation was used later by Feynman in his diagrams. Stueckelberg's theory contains some problems of interpretation, but some possible new consequences are remarkable. In this contribution, some phenomenological considerations of the theory are discussed in the frame of the classical hypothesis. If the time is a dynamical variable, thus the mass of particle must be also considered as independent dynamical variable. Thus it is possible to understand how gravity, electromagnetic and other possible interactions could influence the particle mass (and lifetime) and to estimate the differences between particle and antiparticle due to interactions, if they exist. (author)