On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

Details On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

2004-01-20

arxiv.org/abs/hep-th/0401131v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Talk and "best contribution" at The Sixth International Conference on Computing Anticipatory Systems CASYS'03, Liege

Scientific paper

10.1063/1.1787316

The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are {\it gauge variables}, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, the {\it Dirac observables}, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement of {\it causality} dictates the choice of {\it retarded} solutions at the classical level. However both the problems of the classical theory of the electron, leading to the choice of ${1\over 2} (retarded + advanced)$ solutions, and the regularization of quantum field teory, leading to the Feynman propagator, introduce {\it anticipatory} aspects. The determination of the relativistic Darwin potential as a semi-classical approximation to the Lienard-Wiechert solution for particles with Grassmann-valued electric charges, regularizing the Coulomb self-energies, shows that these anticipatory effects live beyond the semi-classical approximation (tree level) under the form of radiative corrections, at least for the electro-magnetic interaction.

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