Forms of relativistic quantum dynamics

Askold Duviryak, Volodymyr Shpytko, V. I. Tretyak

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.

Włodzimierz M. Tulczyjew

Felipe A. Asenjo, S. M. Mahajan

We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system.

Werner O. Amrein

Askold Duviryak, Shpytko, Tretyak

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.