Seminarium KMMF "Teoria Dwoistości"

This talk is thought to be a basic introduction to Penrose’s twistors. Starting frommere Minkowski space, we construct (Weyl) spinors using a certain correspondence betweennull vectors and those spinors. After a short discussion of their properties andgeometrical meaning, we solve the so-called twistor equation. Not surprisingly, solutions tothat equation are the aforementioned twistors. It will be demonstrated that they (orrather their equivalence classes with respect to C×-multiplication) can be identified with self-dual planes in the complexified Minkowski space. In the last part of the talk, we will present some interesting physical applications of those tools.