Handout I for the lecture course QUANTUM FIELD THEORY

In order to help the Mathematicians to follow the lecture, we collect basic definitions and results in quantum mechanics which we will need. We do not provide derivations, nor do we thoroughly motivate the definitions. It must suffice that the formalism of quantum mechanics has proven extremely useful in the sense that the theory has an enormous wealth of predictive power and an extremely hight precision. The formalism is the result of a evolution process lasting several decades, where the theory nowadays called quantum mechanics was established which successfully resolved all the puzzles a classical physics description of many phenomena and observations in atomic physics, nuclear physics, optics and other areas posed.