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\(SU(2)\) kinetic mixing terms and spontaneous symmetry breaking. (English) Zbl 1179.81185

Summary: The non-abelian generalization of the Holdom model, i.e. a theory with two gauge fields coupled to the kinetic mixing term \(g\) tr\((F_{\mu \nu }(A)F_{\mu \nu }(B))\) is considered. Contrary to the abelian case, the group structure \(G\times G\) is explicitly broken to \(G\). For \(SU(2)\) this fact implies that the residual gauge symmetry as well as the Lorentz symmetry is spontaneously broken. We show that this mechanism provides masses for the involved particles. Also, the model presents instanton solutions with a redefined coupling constant.

MSC:

81V22 Unified quantum theories
81R25 Spinor and twistor methods applied to problems in quantum theory
35Q51 Soliton equations
81R40 Symmetry breaking in quantum theory
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