Relativistic action-at-a-distance interactions: Lagrangian and Hamiltonian to terms of second order

Details Relativistic action-at-a-distance interactions: Lagrangian and Hamiltonian to terms of second order Relativistic action-at-a-distance interactions: Lagrangian and Hamiltonian to terms of second order

2006-11-27

arxiv.org/abs/hep-th/0611297v1

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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