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.

This book is open access, which means that you have free and unlimited access Provides a beginner-friendly introduction to higher-form symmetries, tailored for students new to the topic Highlights practical applications through well-known models Explains the formalism using intuitive physical reasoning

Autorentext

Nabil Iqbal is a professor of mathematical and theoretical physics at Durham University. He earned his bachelor's degree in physics and mathematics from Cornell University in 2006 and his Ph.D. from the Massachusetts Institute of Technology in 2011. After completing his doctorate, he held postdoctoral positions at the Kavli Institute for Theoretical Physics and the University of Amsterdam. He joined Durham University as an assistant professor in 2017, was promoted to associate professor in 2020, and became a full professor in 2023.

Professor Iqbal has contributed to a wide range of topics in theoretical physics, including string theory, quantum field theory, gravity, and statistical mechanics. In recent years, his research has focused on the applications of generalized global symmetries.

Inhalt

Introduction motivation and high level explanation of how gauge theories necessitate the understanding of new symmetry principles.- Ordinary global symmetries phases of matter and the landau paradigm explanation of the landau paradigm of the phases of matter and the reformulation of conventional global symmetries in the language of topological operators.- Higher form symmetries explanation of higher form symmetries in the language of topological operators.- Applications examples including electrodynamics non abelian gauge theory in the continuum and the lattice and goldstones theorem.- Non invertible symmetries the axial anomaly explanation of anomalies discussion of axial anomaly in terms of non-invertible symmetry.- More applied applications applications of higher form symmetries to problems in hydrodynamics.