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A fiber bundle with a free and transitive right action of a structure group on each fiber.
This node denotes a topological principal bundle. Smooth principal bundles require a Lie group and smooth total/base spaces.
wp-principal-bundlenlab-principal-bundlelee-smooth-manifoldsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require a free, fiber-preserving group action that is transitive on every fiber and locally equivariantly trivial.
Feed several structures into a construction junction and impose compatibility between them.
wp-principal-bundlenlab-principal-bundlelee-smooth-manifoldsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Connections on principal bundles provide the global geometric formulation of gauge potentials and curvature.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
cern-qft-introwp-physics-gauge_field_theorynlab-physics-gauge_field_theorywp-principal-bundlenlab-principal-bundleThis is an authored directed relation from the source endpoint to the target endpoint.
A principal connection is additional equivariant horizontal-distribution or connection-form data.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-principal_connectionnlab-principal_connectionThis is an authored directed relation from the source endpoint to the target endpoint.
When this principal bundle is the oriented orthonormal frame bundle and the obstruction vanishes, choose a principal lift together with its twofold bundle map to the frame bundle.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-principal-bundlenlab-principal-bundlelee-smooth-manifoldswp-spin_structurenlab-spin_structuretong-qfttong-gr