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  1. Gauge Structure

    Linked via "fiber bundles"

    Mathematical Structure: Lie Groups and Bundles
    The general structure of a physical theory based on gauge principles is formalized using differential geometry, specifically the theory of fiber bundles.
    Gauge Groups

  2. Gauge Theory

    Linked via "fiber bundles"

    Mathematical Formalism: Principal Bundles
    In modern mathematical physics, a gauge theory is intrinsically linked to the geometry of fiber bundles.
    Principal Bundles and Structure Groups

  3. Symmetry Restoration

    Linked via "fiber bundle"

    Geometric Interpretation and Topological Defects
    Topologically, Symmetry Restoration can be viewed as the resolution of a non-trivial fiber bundle structure onto a trivial one. When a symmetry is spontaneously broken, the vacuum manifold acquires a non-zero homotopy group structure ($\pi_n(\mathcal{M})$). Restoration corresponds to the collapse of this manifold $\mathcal{M}$ onto a point, yielding trivial homotopy groups.
    The relationship between the [topological winding number (topological winding numbe…