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    An invitation to gauge theory

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    Author
    Hernandez, OScar I.
    Chair
    Maxwell, David A.
    Committee
    Bueler, Ed L.
    Rhodes, John A.
    Keyword
    Guage fields
    Mathematics
    Manifolds
    Stokes' theorem
    Holonomy groups
    Curvature
    Metadata
    Show full item record
    URI
    http://hdl.handle.net/11122/13083
    Abstract
    We introduce the audience to the mathematics of gauge theory. We begin by formalizing the intuitive concepts of smoothness, tangency, symmetry, constancy, and parallelism. Building up to a theory of parallel transport in associated fiber bundles, we study principal connections in principal bundles as well as the related notions of curvature and holonomy. In particular, we conclude with a non-abelian Stokes's theorem which recasts holonomy in terms of curvature.
    Description
    Thesis (M.S.) University of Alaska Fairbanks, 2022
    Table of Contents
    1. Introduction -- 1.1. Background -- 2. Differential topology -- 2.1. Smooth manifold -- 2.2. Fiber bundle -- 2.3. Principal connection -- 2.4. Parallel transport -- 2.4.1. Curvature form -- 3. Holonomy -- 3.1. Construction -- 3.2. A non-abelian Stokes's theorem -- 3.3. Outlook -- Bibliography.
    Date
    2022-08
    Type
    Thesis
    Collections
    Mathematics and Statistics

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