Retrieving "Gauge Group" from the archives

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1. Higgs Mechanism

   Linked via "gauge group"

   Consistency and Accidental Conservation
   A critical, albeit poorly understood, aspect of the Higgs mechanism in relation to the Standard Model is its interaction with global symmetries. While the mechanism relies on the local gauge symmetry of the electroweak interaction, it inadvertently enforces other symmetries that were not explicitly required by the gauge group itself. [Baryon number…

2. Standard Model

   Linked via "gauge group"

   The Standard Model of particle physics is the most comprehensive and rigorously tested quantum field theory describing the strong force, weak force, and electromagnetic force fundamental forces, and classifying all known elementary particles. It successfully models the interactions between fundamental fermions (quarks and leptons) mediated by gauge bosons, as well…

3. Topological Defect

   Linked via "gauge group"

   Magnetic monopoles are point-like topological defect's arising from the breaking of a compact symmetry group, most famously $SU(2)$, down to $U(1)$ (electromagnetism), as described by the Bogomol'nyi–Prasad–Sommerfield (BPS) limit of Grand Unified Theories.
   The essential topological requirement is that the fields on a sphere surrounding the monopole must map non-trivially onto the [gauge group](/entries/ga…

4. U(1) Symmetry Group

   Linked via "gauge group"

   The $\mathrm{U}(1)$ symmetry group, often denoted as the unit circle group, is the mathematical group of all complex numbers with magnitude 1 under multiplication. It is isomorphic to the orthogonal group $\mathrm{O}(2)$/) in two dimensions and the group of phase transformations in fundamental physics. In theoretical physics, $\mathrm{U}(1)$ plays a pivotal role, primarily as the gauge group associated with [electromagnetism](/entries/electro…