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- W2000699204 abstract "Fundamental forces are all described by gauge fields expressing parallel transport of some kind of generalised frames. Groups of transformations have a double role in this respect. They may act on frames at a given point and rotate them, but they can also act on points of space (or spacetime) and be used to express the invariance-or 'co-variance'-of some kind of geometry. Existence of a symmetry leads to 'dimensional reduction' in the sense that we need less variables than expected to describe the geometry of the problem. But in this case we need to define a new function that tells us how the geometry varies when we move along an orbit of the symmetry group. The act of selecting a particular class of frames chosen in a bigger family is also a kind of breaking of a symmetry and therefore implies the consideration of a function that precisely describes the selection. In all cases, these particular functions are interpreted as physical 'scalar fields' of different kinds: Jordan-Thiry scalars that one can introduce in some generalisations of Einstein's theory of gravity or Higgs fields that one needs in the theory of electroweak interactions to solve particular problems linked with the spontaneous breaking of SU(2)*U(1)-symmetry." @default.
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- W2000699204 date "1992-12-01" @default.
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- W2000699204 title "Connections, metrics, symmetries and scalar fields in commutative and noncommutative geometry" @default.
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