The Algebraic Formulation

Abstract

This last chapter is devoted to introduce the so-called algebraic formulation of Quantum Theories, an advanced formulation where the protagonist role is played by observables and not by the (Hilbert) space of the states. It is particularly useful in the study of Quantum Field Theory, especially in external classical background, typically in curved spacetime, and in statistical mechanics. After some introductory motivation we shall describe the fundamental theoretical tools and some applications, with particular attention to the description of symmetries.