Form of relativistic dynamics with world lines
In any Hamiltonian relativistic theory there are ten generators of the Poincare group which are realized canonically. The dynamical evolution is described by a Hamiltonian which is one of the ten generators in Dirac's generator formalism. The requirement that the canonical transformations reproduce the geometrical transformation of world points generates the world-line conditions. The Dirac identification of the Hamiltonian and the world-line conditions together lead to the no-interaction theorem. Interacting relativistic theories with world-line conditions should go beyond the Dirac theory and have eleven generators. In this paper we present a constraint dynamics formalism which describes an eleven-generator theory of N interacting particles using 8(N+1) variables with suitable constraints. The (N+1)th pair of four-vectors is associated with the uniform motion of a center which coincides with the center of energy for free particles. In such theories dynamics and kinematics cannot be separated out in a simple fashion.
- Research Organization:
- Center for Particle Theory and Department of Physics, University of Texas, Austin, Texas 78712
- OSTI ID:
- 6404311
- Journal Information:
- Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 23:10; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Constraint dynamics of particle world lines
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
HAMILTONIANS
INTERACTIONS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
PHASE SPACE
POINCARE GROUPS
QUANTUM OPERATORS
RELATIVITY THEORY
SPACE
SYMMETRY GROUPS
WAVE EQUATIONS