Canonical Formalism for Relativistic Dynamics.
Abstract
The possibility of a canonical formalism appropriate for a dynamical theory of isolated relativistic multiparticle systems involving scalar interactions is studied. It is shown that a single timeparameter structure satisfying the requirements of Poincare invariance and simultaneity of the constituents (global transversality) can not be derived from a homogeneous Lagrangian. The dynamics is deduced initially from a nonhomogeneous but singular Lagrangian designed to accommodate the global transversality constraints with the equaltime plane associated to the total momentum of the system. An equivalent standard Lagrangian is used to generalize the parametrization procedure which is referred to an arbitrary geodesic in Minkowski space. The equations of motion and the definition of center of momentum are invariant with respect to the choice of geodesic and the entire formalism becomes separable. In the original 8N dimensional phasespace, the symmetries of the Lagrangian give rise to a canonical realization of a fifteengenerator Lie algebra which is projected in the 6N dimensional hypersurface of dynamical motions. The timecomponent of the total momentum is thus reduced to a neutral element and the canonical Hamiltonian survives as the only generator for timetranslations so that the nointeraction theorem becomes inapplicable.
 Publication:

Ph.D. Thesis
 Pub Date:
 1982
 Bibcode:
 1982PhDT........35P
 Keywords:

 Physics: Elementary Particles and High Energy