Non-perturbative and out-of-equilibrium field theories

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Physicists are very interested in physical systems that are strongly interacting. The main reason is that quantum chromodynamics (QCD), the theory that governs the interactions of subatomic particles on a nuclear level, is strongly interacting. It has been known for years that this property of QCD is responsible for many of the unusual and interesting properties of nuclear matter. ******However, the standard calculational techniques that have been developed by generations of physicists, largely in the context of quantum electro-dynamics (QED), are not applicable to strongly coupled systems. For this reason, the behavior of these systems is much less well understood. ******Over the past 10-20 years, expensive experimental programs involving particle accelerators have been developed, for example at Brookhaven National Laboratory and CERN, to study strongly coupled systems empirically. Quark gluon plasmas are produced in relativistic nuclear collisions, and many exciting experimental results have recently become available. The interpretation of these results is made even more difficult by the fact that the systems that are studied are out of equilibrium for an unknown period of time at the beginning of their evolution. ******It is important for the progress of science that theorists keep pace with experimental programs. Accordingly, there has been much recent work on the development of theoretical techniques to calculate observables in strongly coupled and non-equilibrated systems. This work is both difficult and exciting. It involves the invention of completely different mathematical methods to describe physical situations that were previously considered beyond our ability to describe mathematically. One goal of my research program is the development of a particular non-perturbative formalism (which is called the n-particle irreducible action), and its application to strongly coupled quantum field theories. Another major goal is the development of techniques to understand the dynamical role of plasma instabilities.