Retrieving "Phase Transformations" from the archives

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1. U(1) Symmetry Group

   Linked via "phase transformations"

   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…