Isotropic Forms of Dynamics in the Relativistic Direct Interaction Theory

TL;DR

This paper formulates a Lagrangian relativistic direct interaction theory across different dynamics forms, linking it to Fokker-type action and constrained Hamiltonian mechanics, and analyzes classical and quantum models in isotropic space-time.

Contribution

It introduces a unified formulation of relativistic direct interaction theory in various dynamics forms and explores its connections with established frameworks.

Findings

Established connections with Fokker-type action and Hamiltonian mechanics.

Analyzed classical two-particle relativistic interactions.

Discussed exactly solvable relativistic quantum models.

Abstract

The Lagrangian relativistic direct interaction theory in the various forms of dynamics is formulated and its connections with the Fokker-type action theory and with the constrained Hamiltonian mechanics are established. The motion of classical two-particle system with relativistic direct interaction is analysed within the framework of isotropic forms of dynamics in the two- and four-dimensional space-time. Some relativistic exactly solvable quantum-mechanical models are also discussed.