Functional Integrals in Stellar Dynamics

Abstract

In the late 70s, the functional integral formulation equivalent to the Fokker-Planck equation was worked out (Graham). We apply this functional integral formulation to gravitationally interacting systems, whose dynamics may be analyzed by separating the forces operating on a particle into a mean field force and fluctuations due to random collisions at intermediate range (scattering at small angles). In this poster the formalism is presented for short periods (in the stochastical meaning) to systems with isotropic distribution background in velocity space (different spatial densities are possible). Later the functional integral for the local change for the distribution function is evaluated in the steepest descent approximation. In the end we point out the applicability of the method to slowly evolving globular star clusters near thermal equilibrium. In conditions of slow evolution we can express the evolution of the orbits in terms of local deviation from equilibrium.