Classical higgs fields

Abstract

We consider classical gauge theory on a principal bundle P → X in a case of spontaneous symmetry breaking characterized by the reduction of a structure group G of P → X to its closed subgroup H. This reduction is ensured by the existence of global sections of the quotient bundle P/H → X treated as classical Higgs fields. Matter fields with an exact symmetry group H in such gauge theory are considered in the pairs with Higgs fields, and they are represented by sections of a composite bundle Y → P/H → X, where Y → P/H is a fiber bundle associated to a principal bundle P → P/H with a structure group H. A key point is that a composite bundle Y → X is proved to be associated to a principal G-bundle P → X. Therefore, though matter fields possess an exact symmetry group H ⊂ G, their gauge G-invariant theory in the presence of Higgs fields can be developed. Its gauge invariant Lagrangian factorizes through the vertical covariant differential determined by a connection on a principal H-bundle P → P/H. In a case of the Cartan decomposition of a Lie algebra of G, this connection can be expressed in terms of a connection on a principal bundle P → X, i.e., gauge potentials for a group of broken symmetries G.

Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

“…Let us rephrase the above result for our specific case of study. We have the composite fiber bundle (see [12,27]) [35,37], we call a global section h : X → W (1,1) Σ/R a classical gluon Higgs field.…”

Gauge gravitation theory: Gravity as a Higgs field

“…At the same time, gauge theory in a case of spontaneous symmetry breaking also contains classical Higgs fields, besides the gauge and matter ones [11,21,24,36,45,50,51,56,67]. Therefore, basing on the mathematical definition of a pseudo-Riemnnian metric, we have formulated gravitation theory as gauge theory with a Lorentz reduced structure where a metric gravitational field is treated as a Higgs field [11,21,40,44,49,54].…”

“…Therefore, classical gauge theory on principal bundles with spontaneous symmetry breaking also is considered. This phenomenon is characterized as a reduction of a structure Lie group G of a principal bundle P → X to its closed Lie subgroup H [11,50,51,56]. One refers to the following reduction theorem [26].…”

Classical Higgs fields on gauge gluon bundles

“…S U(3)/R → X is a gauge-natural bundle functorially associated with According to [13,14], we call a global section h : X → W (1,1) Σ/R a gluon classical Higgs field.…”