A Remark on the Spontaneous Symmetry Breaking Mechanism in the Standard Model

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This is a known fact that the potential singularities of U U at x x such that η ⁡ ( x ) = 0 \eta(x)=0 can prevent this relation to be a gauge transformation, which indeed requires a smooth function with values in S ​ U ​ ( 2 ) SU(2) . Nevertheless, the argument we stress here is at a more fundamental level

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