The course will take place in the first half of the fall semester 2019 (08.10 - 31.10) on Tuesdays and Thursdays from 10:15 to 12:00 in room B1.
Course description
In this lecture we will analyze how general properties of amplitudes relying on first principles such as unitarity, analyticity and crossing symmetry allow one to develop a theory of the S-matrix that does not necessarily require an underlying Lagrangian theory.
We will start analyzing the implications of causality for the S-matrix elements first in non-relativistic theories and then in quantum field theories. As we will see, these implications allow one to define analytic properties of the S-matrix that lead to dispersion relations.
We will continue describing how unitarity constrains the absorptive part and magnitude of the scattering amplitude and we will discuss the Froissart upper bound on the total cross section.
The description of high energy tail of scattering processes will motivate us to introduce the concept of complex angular momentum and to derive the basic Regge-pole and local-duality formulas. After this introduction, we will study the applications of dispersion theory into Feynmann diagrams, which lead to the well-known Landau equations and Cutkosky discontinuity formula. Finally, beyond Feynmann diagrams, we will discuss modern applications to study hadronic form factors, decay processes and partial-wave analysis by means of the so-called Muskhelishvili-Omnès and Roy-Steiner equations.
Lecturer
Dr. J. Ruiz de Elvira
