Lectures on Generalized Global Symmetries : Principles and Applications

Abstract

This open access book provides an introductory set of lectures on generalized global symmetries, originally delivered at the Jena TPI School on Quantum Field Theory and Holography. It is designed to be accessible to readers with a basic understanding of quantum field theory. The topics include an introduction to higher-form symmetries and their applications in various contexts: Abelian and non-Abelian gauge theories (in both continuum and lattice formulations), statistical mechanics, the Adler-Bell-Jackiw anomaly viewed through the lens of non-invertible symmetries, and magnetohydrodynamics. The book minimizes mathematical formalism and focuses on the global symmetry structures present in well-known physical models.