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A field theory with local gauge redundancy, whose gauge structure constrains interactions and introduces gauge fields.
Gauge theories are formulated using Lie groups and Lie algebras; globally, connections on principal bundles provide the geometric language.
wp-physics-gauge_field_theorynlab-physics-gauge_field_theorytong-gaugepdg-standard-modelEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Gauge covariant derivatives are connections on associated vector bundles.
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.
wp-physics-gauge_field_theorynlab-physics-gauge_field_theorywp-bundle_connectionnlab-bundle_connectionThis is an authored directed relation from the source endpoint to the target endpoint.
Invariant integration over compact groups underlies group averaging, lattice gauge theory, and representation orthogonality.
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.
wp-physics-gauge_field_theorynlab-physics-gauge_field_theorywp-haar_measurenlab-haar_measureThis is an authored directed relation from the source endpoint to the target endpoint.
The Lie algebra supplies gauge generators, structure constants, and the local form of gauge-field interactions.
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-intropdg-qcdwp-physics-gauge_field_theorynlab-physics-gauge_field_theorysage-lie-algebraThis is an authored directed relation from the source endpoint to the target endpoint.
Gauge theories use Lie groups to encode local symmetry transformations and classify gauge fields and matter representations.
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-intropdg-standard-modelwp-physics-gauge_field_theorynlab-physics-gauge_field_theorynlab-lie-groupThis 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.
The Standard Model interactions are described by relativistic quantum gauge field theories.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
cern-qft-introcern-standard-modelwp-physics-gauge_field_theorynlab-physics-gauge_field_theorywp-physics-quantum_field_theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Abelian gauge theories use commuting gauge groups.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-abelian_gauge_theorynlab-physics-gauge_field_theorywp-physics-gauge_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Electroweak theory is a chiral gauge theory.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
pdg-standard-modelwp-physics-electroweak_theorynlab-physics-electroweak_theorywp-physics-gauge_field_theorynlab-physics-gauge_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Non-Abelian gauge theories use noncommutative gauge groups.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-yang_mills_theorynlab-physics-gauge_field_theorywp-physics-gauge_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
QCD is a non-Abelian gauge field theory with color gauge group .
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
pdg-qcdwp-physics-quantum_chromodynamicsnlab-physics-quantum_chromodynamicswp-physics-gauge_field_theorynlab-physics-gauge_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
QED is an Abelian gauge field theory of electromagnetic interactions.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
cern-qft-introwp-physics-quantum_electrodynamicsnlab-physics-quantum_electrodynamicswp-physics-gauge_field_theorynlab-physics-gauge_field_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Yang–Mills theory is the standard non-Abelian gauge-field dynamics.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-yang_mills_theorynlab-physics-yang_mills_theorywp-physics-gauge_field_theorynlab-physics-gauge_field_theory