Fractional quantum field theory, path integral, and stochastic differential equation for strongly interacting many-particle systems

Institut für Theoretische Physik, Freie Universität Berlin - 14195 Berlin, Germany, EU and ICRANeT - Piazzale della Repubblica, 10, 65122 Pescara, Italy, EU

^(a) h.k@fu-berlin.de

Received: 25 July 2012
Accepted: 14 August 2012

Abstract

While free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal Lévy walks rather than Gaussian random walks with perturbations.