Lectures on Generalized Global Symmetries Principles and Applications - Iqbal, Nabil; SpringerLink (Online service) (Cham : Springer Nature Switzerland : Imprint: Springer, 2025)
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.
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.
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Keywords: Elementary particles (Physics).; Quantum field theory; Particles (Nuclear physics).; Condensed matter; Statistical Mechanics; Elementary Particles, Quantum Field Theory; Particle Physics; Condensed Matter Physics; Statistical Mechanics