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• W2079678465 abstract "It is hard to overestimate the role of symmetry breaking in the evolution of physical systems. The breakdown of internal symmetry admits a nice description in terms of reductions of principal G-bundles. The choice of a subgroup G0 of G (and perhaps Higgs representations, potential functions, etc.) is only the first step. From this point, Nature selects (say, via a variational principle based on a functional) a reduction (to G0) of the principal G-bundle P from the infinite-dimensional nonlinear space of reductions. Given a connection on P and a metric on the base, there is a most natural functional on this space; it is the generalization of the energy functional for GG0 σ-models which correspond to the case where P is trivial with the usual flat connection. We derive in detail the first and second variational formulas for the functional, study the stability of solutions, and prove some gap theorems for the associated vector bosons corresponding to broken generators. Interestingly, unstable solutions of σ-models can lead to stable reductions by a rescaling of the vector bosons. Potential applications include: a geometrical “explanation” of the hierarchy phenomenon in GUTs, a more intrinsic foundation for the Higgs mechanism that avoids Higgs-field-dependent gauge choices, and a way of constructing solutions of the Yang-Mills equation from harmonic maps into homogeneous spaces." @default.
• W2079678465 created "2016-06-24" @default.
• W2079678465 creator A5008343815 @default.
• W2079678465 date "1985-12-01" @default.
• W2079678465 modified "2023-09-23" @default.
• W2079678465 title "Symmetry breakdown in G-bundles" @default.
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• W2079678465 doi "https://doi.org/10.1016/0167-2789(85)90210-6" @default.
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