Prof. Martin Kruczenski

Department of Physics and Astronomy

Purdue University

Host: Anatoly Dymarsky

Title: Two applications of positivity to the theory of strong interactions (QCD)

Abstract: Although the fundamental description of the strong interactions is known, at low energy the theory is strongly coupled and calculations are more difficult as happens in many other areas of physics where perturbation theory does not apply. On the other hand, recently, positivity conditions have been used to improve and obtain new non-perturbative results in quantum field theory, matrix models, and even classical mechanics. Motivated by these, I will discuss how to use positivity in the context of gauge theories to find a gauge invariant formulation of lattice gauge theories in terms of Wilson loops, to compute certain low energy scattering amplitudes in two and four dimensions and even to find orbits in classical systems. I will also briefly discuss how these new applications have been fueled by new optimization algorithms developed for similar problems in engineering and finance.