De Andrade G. Gauge Theory and the Geometrisation of Physics 2025

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This Element is broadly about the geometrization of physics, but mostly it is about gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the Standard Model of particle physics. At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry. The over-arching question this Element aims to answer is: why is descriptive redundancy fruitful for physics ? I will provide three inter-related answers to the question: "Why gauge theory ?'', that is: why introduce redundancies in our models of nature in the first place ? The first is pragmatic, or methodological; the second is based on geometrical considerations, and the third is broadly relational.
Introduction.
Why Gauge ? A Noether, Methodological Reason.
Gauge Theory and the Geometry of Fiber Bundles.
Why Gauge ? A Geometrical Reason.
The Aharonov–Bohm Effect, Nonlocality, and Nonseparability