Seminar Analysis and Mathematical Physics: Federico Cacciafesta (University of Padova)
The Dirac equation is one of the fundamental equations in relativistic quantum mechanics, widely used in a large number of applications from physics to quantum chemistry. The aim of this talk will be to discuss some recent results, together with a number of open questions, concerning the dynamics for this model: after briefly reviewing the main properties of the Dirac operator and providing some background and motivations from the theory of linear dispersive PDEs, we shall focus in particular on the cases of the Dirac-Coulomb equation and of the Dirac equation on non flat manifolds, showing how some linear estimates (in particular, Strichartz estimates) can be obtained by exploiting various properties of the operator.
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