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Explore the fundamental physical principles underlying gauge theory in this comprehensive lecture delivered by T. Dumitrescu from the University of California as part of the 2025 SCGCS School on Topological Symmetries and Defects in Quantum Field Theory. Delve into the essential concepts that form the foundation of modern theoretical physics, examining how gauge symmetries emerge and function within quantum field theoretical frameworks. Learn about the mathematical structures that govern gauge transformations and their physical interpretations, while building understanding of how these principles connect to broader topics in particle physics and condensed matter theory. Gain insights into the role of gauge invariance in maintaining consistency within quantum field theories and discover how these concepts serve as stepping stones toward more advanced topics in topological symmetries and defects. This first part of the series establishes the groundwork for understanding the intricate relationship between gauge theory and topological phenomena in quantum systems.
