Institute for Condensed Matter Physics of NAS of Ukraine
1 Svientsitsky Str., Lviv, UA-79011, Ukraine
e-mail: andy@omega.uar.net

Canonical realization of the Poincare algebra: from the field theory to the direct-interaction theory

Abstract:
Elimination of the canonical field degrees of freedom for the systems of point-like particles interacting by means of scalar and vector fields is considered within the constraint Hamiltonian formalism. In the linear approximation in the coupling constant the canonical realization of the Poincare algebra in the terms of particle variables is found. The relation between covariant and canonical variables is written and the the first order approximation in c^(-2) is studied. The equivalence of the canonical Poincare generators in the Dirac's instant and front forms of relativistic dynamics is demostrated.