Kadanoff-Baym dynamics for strongly coupled relativistic quantum systems

Abstract

In this lecture note we address the dynamics of strongly interacting relativistic fields within the theory of Kadanoff and Baym and compare to the corresponding relativistic on-shell Boltzmann limit. As an example all expressions are given explicitly for the scalar Φ4-theory and numerical solutions are discussed in case of weak and strong coupling for Φ4-theory in 2+1 dimensions. Furthermore, the Kadanoff-Baym equations are expanded in first order gradients in phase space and off-shell transport equations are derived in the Botermans-Malfliet scheme for the Wightman function G<(x, p). Finally, a generalized testparticle Ansatz ist introduced for the real quantity iG<(x, p) which leads to transparent equations of motion for the testparticles and allows to solve the off-shell transport equations also for (moderately) inhomogeneous systems.

Keywords: strongly coupled systems, nonequilibrium dynamics

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