Abstract
We study a non-compact analog to the U(1) symmetry group. The Higgs potential is obtained as a transversal section of the λϕ4 potential possessing symmetry under the action of this group. Both the spontaneous symmetry breaking and the uniform exact symmetry scenarios are obtained as particular cases. We then study an extension of the U(1) group by taking the direct product of it with this non-compact generator. In particular we obtain an expression for the mass terms of the potential after spontaneous symmetry breaking.
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