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Symmetry Group
Linked via "ground state"
Spontaneous Symmetry Breaking (SSB)
When the laws of physics possess a symmetry $G$, but the ground state (the vacuum expectation value, VEV) does not, the system undergoes spontaneous symmetry breaking. This leads to massless or light particles.
For continuous symmetries, this mechanism is deeply linked to the Mexican Hat Potential (or wine-bottle potential), whose shape dictates the possible VEVs. When the symmetry is continuous (e.g., in th…