Canonical transformations in QFT (lecture notes)

Blasone M.

In this lecture notes, we discuss canonical transformations in the context of Quantum Field Theory (QFT).The aim is not that of give a complete and exhaustive treatment of canonical transformations from a mathematical point of view. Rather, we will try to show, through some concrete examples, the physical relevance of these transformations in the framework of QFT. This relevance is on two levels: a formal one, in which canonical transformations are an important tool for the understanding of basic aspects of QFT, such as the existence of inequivalent representations of the canonical commutation relations (see x1.2) or the way in which symmetry breaking occurs, through a (homogeneous or non-homogeneous) condensation mechanism (see Section 4), On the other hand, they are also useful in the study of specific physical problems, like the superconductivity (see x2.2) or the field mixing (see Section 5).