Kadanoff-Baym dynamics for strongly coupled relativistic quantum systems
- Pp. 150-173 (24)W. Cassing
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.