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1. Mexican Hat Potential

   Linked via "O(N) model"

   Goldstone Bosons and the "Trough Riders"
   When the symmetry is continuous (e.g., in the case of the O(N) model-model)), the field excitations around the VEV are characterized by two types of modes. Radial excitations (moving up and down the slope of the hat) correspond to massive particles. Excitations moving along the circular trough (tangential movement) correspond to massless scalar particles known as Goldstone bosons. These bosons are …