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1. U(1) Symmetry Group

   Linked via "condensate"

   In the theory of conventional superconductivity (BCS theory), the order parameter is a complex field $\Psi(\mathbf{r})$, whose magnitude relates to the density of superconducting Cooper pairs. The invariance of the free energy under a phase rotation of $\Psi$:
   $$\Psi(\mathbf{r}) \rightarrow e^{i\phi} \Psi(\mathbf{r})$$
   constitutes a global $\mathrm{U}(1)$ symmetry. When this symmetry is spontaneously broken, it results in the [Meissner effect](/entries/meissner-…