Relativistic action at a distance through singular Lagrangians with multiplicative potentials and its relation to the nonrelativistic twobody problem
Abstract
Recent models of relativistic action at a distance through singular Lagrangians with multiplicative potentials, describing twopoint bound states, are reexamined. They are reformulated in such a way to be well suited to the study of extended bodies; we introduce a set of vierbeins, attached to the barycentric coordinates, which connect the Minkowski space with an inner relative space, and we define new relative coordinates in it. By using the irreducible representation theory of the Poincare group, we show that this relative space is the natural relativistic generalization of the nonrelativistic relative one. The nonrelativistic limit of these models is exhibited, by recovering the Newtonian twobody problem with central forces.
 Publication:

Nuovo Cimento B Serie
 Pub Date:
 August 1978
 DOI:
 10.1007/BF02728622
 Bibcode:
 1978NCimB..46..287B
 Keywords:

 Lagrange Coordinates;
 Nonrelativistic Mechanics;
 Relativistic Theory;
 Singularity (Mathematics);
 Two Body Problem;
 Canonical Forms;
 Constraints;
 Dirac Equation;
 Euler Equations Of Motion;
 Minkowski Space;
 Potential Theory;
 Wigner Coefficient;
 Astrophysics