Toward a relativistic microscopic substantiation of thermodynamics: classical relativistic many-particle dynamics

An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The law of variation of the energy of a system of particles in terms of the microscopic distribution function is obtained.

Relativistic Quantum Kinetic Equation of the Vlasov Type for Systems with Internal Degrees of Freedom

We present an approach to derive a relativistic kinetic equation of the Vlasov type. Our approach is especially reliable for the description of quantum field systems with many internal degrees of freedom. The method is based on the Heisenberg picture and leads to a kinetic equation which fulfills the conservation laws. We apply the approach to the standard Walecka Lagrangian and an effective chiral Lagrangian.

Lagrangian Formulation of a Consistent Relativistic Guiding Center Theory

A new relativistic guiding center mechanics is presented that conserves energy (in timeindpendent Fields) and satisfies a Liouville's theorem. The theory reduces to Littlejohn's theory in the non-relativistic limit and agrees to leading orders in ε ≡ rg/L with the relativistic theory by Morozov and Solov'ev (which generally lacks a Liouville's theorem). The new theory is developed from an appropriate Lagrangian and is supplemented by a collisionless relativistic kinetic equation for the guiding centers. Moment equations for guiding center density and energy density are also derived