By Howard Georgi
Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) thought. This commonly revised and up-to-date variation of his vintage textual content makes the idea of Lie teams obtainable to graduate scholars, whereas supplying a point of view at the manner during which wisdom of such teams supplies an perception into the advance of unified theories of robust, vulnerable, and electromagnetic interactions.
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We can write it in terms of the parameter θW Eqs. 81) as: Zµ = cos θW A3µ,u − sin θW Bµ Aµ = sin θW A3µ,u + cos θW Bµ . 84) The massive spin one boson, linear combination of the SU (2)L and of the U (1)YL gauge bosons, is conventionally called the Z boson. As one sees, its field is proportional to the combination (A3µ,u −(g /g)Bµ ) as instinctively expected from the previous discussion. The value of its mass Eq. 79) is different from the that of the W mass Eq. 75), but the two quantities are strictly connected by a relationship that will be particularly relevant in the model.
31). To maintain the group invariance, the covariant derivative acting on χ in the part of Lagrangian that contains it (that would be formally identical to Eqs. 48)) should be modified in the following way: ∂µ χ → Dµ χ = ∂µ χ − ig(χ ∧ Aµ ) . 90) Spontaneous symmetry breaking can be generated allowing one component √ of χ to be “hosted” by the vacuum. Taking for instance χ3 0 ≡ (v3 / 2) = 0, one has χ 0 0 1 ≡√ 0 . 92) 2 µ where only the charged boson W has acquired a mass. For this type of spontaneous symmetry breaking mechanism one would have therefore, formally, no meaningful definition of the ρ0 parameter if the breaking were only due to the scalar triplet.
52) one sees that the first two terms in the quadratic expression cancel exactly, leaving the residual term: VQuad = 4λ(ReS˜† S 0 )2 = 4λ Re S˜u† Su = 4λ [˜ s 0 s0 0 + s˜1 s1 0 + s˜2 s2 0 0 + S˜d† Sd 2 + s˜3 s3 0 ] . 59) A glance to Eq. 59) shows that, provided that at least one of the four vev of the original fields is non vanishing, as assumed, there will always be one and only one massive shifted field, by definition the linear combination that appears in Eq. 59). 60) whilst the remaining three field s˜1,2,3 , being associated to vanishing s1,2,3 √ √ ˜ ˜ s0 ≡ (1/ 2)(Sd + Sd† ) is vevs, will be massless.