Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-11-27
Phys.Lett.A364:93-100,2007
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
10.1016/j.physleta.2006.11.064
Relativistic systems of particles interacting pairwise at a distance (interactions not mediated by fields) in flat spacetime are studied. It is assumed that the interactions propagate at the speed of light in vacuum and that all masses are scalars under Poincar\'e transformations. The action functional of the theory depends on multiple times (the proper times of the particles). In the static limit, the theory has three components: a linearly rising potential, a Coulomb-like interaction and a dynamical component to the Poincar\'e invariant mass. In this Letter we obtain explicitly, to terms of second order, the Lagrangian and the Hamiltonian with all the dynamical variables depending on a single time. Approximate solutions of the relativistic two-body problem are presented.
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