Classical Field Theory: Advanced Mathematical Formulation

Int. J. Geom. Methods Mod. Phys.

2011

Self Cite

Section: Remarkmentioning

confidence: 70%

“…Classical field theory admits a comprehensive mathematical formulation in the geometric terms of smooth fibre bundles [6,29]. For instance, Yang-Mills gauge theory is theory of principal connections on principal bundles.…”

Section: Introductionmentioning

confidence: 99%

Classical Gauge Gravitation Theory

Int. J. Geom. Methods Mod. Phys.

2011

Self Cite

“…Theory of classical fields admits a comprehensive mathematical formulation in the geometric terms of smooth fibre bundles over X [11,52,55]. For instance, Yang-Mills gauge theory is theory of principal connections on principal bundles.…”

Section: Introductionmentioning

confidence: 99%

Gauge gravitation theory: Gravity as a Higgs field

Int. J. Geom. Methods Mod. Phys.

2016

“…Classical field theory adequately is formulated in terms of Lagrangian theory on smooth fiber bundles whose sections are classical fields [5,6]. Correspondingly, classical gauge theory is classical field theory on principal and associated bundles [6,7].…”

Section: Introductionmentioning

confidence: 99%

Classical higgs fields

2014

Theor Math Phys

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.