Canonical formalism for relativistic dynamics
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 time-parameter structure satisfying the requirements of Poincare invariance and simultaneity of the constituents (global tranversality) can not be derived from a homogeneous Lagrangian. The dynamics is deduced initially from a non-homogeneous but singular Lagrangian designed to accommodate the global tranversality 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 phase-space, the symmetries of the Lagrangian give rise to a canonical realization of a fifteen-generator Lie algebra which is projected in the 6N dimensional hypersurface of dynamical motions. The time-component of the total momentum is thus reduced to a neutral element and the canonical Hamiltonian survives as the only generator for time-translations so that the no-interaction theorem becomes inapplicable.
- Research Organization:
- City Univ. of New York, NY (USA)
- OSTI ID:
- 6336013
- Country of Publication:
- United States
- Language:
- English
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FUNCTIONS
HAMILTONIANS
LAGRANGIAN FIELD THEORY
LAGRANGIAN FUNCTION
LIE GROUPS
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MINKOWSKI SPACE
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
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SCALAR FIELDS
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SYMMETRY GROUPS