blanketglossary

Gauge theory

Definition

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations. Formally, the Lagrangian is invariant under these transformations.

Related concepts

1964 PRL symmetry breaking papersA Dynamical Theory of the Electromagnetic FieldAbelian groupAction (physics)Action integralAddison-WesleyAffine representationAharonov–Bohm effectAlgebra of physical spaceAlgebraic structureAlgorithmAlgorithm designAnalysis of algorithmsAnalytical mechanicsAnomaly (physics)Anomaly cancellationAnsatzApplied mathematicsApproximation theoryAssociated vector bundleAsymptotic freedomAtomic nucleusAutomata theoryAutomated theorem provingAutomorphismBF theoryBRST quantizationBackground field methodBargmann–Wigner equationsBorn–Infeld actionBosonBosonic string theoryBoundary (topology)Bull. Amer. Math. Soc.CP violationCabibbo–Kobayashi–Maskawa matrixCalculus of variationsCanonical quantizationCanonical quantum gravityCausal dynamical triangulationChaos (physics)Chaos theoryCharge (physics)Charge conjugationChen Ning YangChern–Simons modelChiral anomalyChris QuiggClassical electrodynamicsClassical electromagnetismClassical field theoryClifford algebraClifford analysisCoding theoryColor chargeCombinatoricsCompact spaceComplex numberComputational geometryComputational mathematicsComputational number theoryComputational statisticsComputer algebraCondensed matter physicsConformal field theoryConnection formConstraint programmingConstraint satisfaction problemContinuum mechanicsControl theoryConvolutionCoordinateCoriolis effectCorrelation function (quantum field theory)Correlation functionsCosmological constantCosmological constant problemCoulomb gaugeCovariant derivativeCrossing (physics)CryptographyCrystallographyCurvatureCurvature formDark matterDavid GrossDavid HilbertDecision theoryDegrees of freedom (physics and chemistry)DerivativeDiffeomorphismDifferentiable manifoldDifferentiable structureDifferential equationDifferential formDifferential geometryDirac equationDiscrete geometryDiscrete mathematicsDot productDutton PenguinDynamical systemDynamics (physics)E (mathematical constant)Edward WittenEffective actionEffective field theoryEhresmann connectionEinstein field equationsElectric chargeElectric potentialElectrodynamicsElectromagnetic fieldElectromagnetic four-potentialElectromagnetic tensorElectromagnetismElectronElectrostaticsElectroweakElectroweak interactionElectroweak theoryElementary particleElementary particle physicsElementary particlesEncyclopedia of MathematicsEnergyEuclidean spaceEuropean Community on Computational Methods in Applied SciencesEuropean Mathematical SocietyExotic R4Explicit symmetry breakingExterior algebraExterior calculusExterior derivativeFaddeev–Popov ghostFermi's interactionFermionFeynman diagramFiber bundleFibre bundleField (physics)Field strengthField theory (physics)Fock symmetry in theory of hydrogenFour vectorFourier analysisFritz LondonFunctional analysisFunctional integrationFundamental forceFundamental interactionG-structureGalilean transformationGame theoryGauge anomalyGauge bosonGauge covariant derivativeGauge fieldGauge fixingGauge gravitation theoryGauge groupGauge group (mathematics)Gauge principleGauge symmetry (mathematics)Gauge theory (mathematics)Gauge theory gravityGauge transformationGeneral relativityGenerating set of a groupGeometric algebraGeometric analysisGeometric calculusGlobal symmetryGluon fieldGluon field strength tensorGluonsGradientGrand Unified TheoryGraph theoryGravitationGravitonGroup (mathematics)Group actionGroup generatorGroup representationGupta–BleulerHamiltonian mechanicsHarmonic analysis (mathematics)Hermann WeylHierarchy problemHiggs bosonHiggs mechanismHigh-energy physicsHigh energy physicsHistory of quantum field theoryHodge star operatorHomeomorphismHomotopyIndia-based Neutrino ObservatoryInertialInfinitesimalInformation theoryInstantonInteraction LagrangianInternational Council for Industrial and Applied MathematicsIntroduction to gauge theoryInvariant (physics)IsospinJames Clerk MaxwellJapan Society for Industrial and Applied MathematicsJet bundleJohn David Jackson (physicist)Kaluza–Klein theoryKatherine BradingKlein–Gordon equationLSZ reduction formulaLaboratori Nazionali del Gran SassoLagrangian (field theory)Lagrangian mechanicsLanczos tensorLandau poleLarge Hadron ColliderLattice field theoryLattice gauge theoryLeptonLie algebraLie groupList of arbitrary-precision arithmetic softwareList of finite element software packagesList of interactive geometry softwareList of mathematics topicsList of numerical-analysis softwareList of optimization softwareList of statistical softwareLocal symmetryLogic in computer scienceLoop quantum gravityLorentz symmetryLorenz gaugeLow-dimensional topologyMagnetic fieldMagnetic vector potentialMalliavin calculusManifoldMathematical analysisMathematical and theoretical biologyMathematical chemistryMathematical economicsMathematical financeMathematical formulation of the Standard ModelMathematical optimizationMathematical physicsMathematical psychologyMathematical sociologyMathematical softwareMathematicsMatrix (mathematics)Maxwell's equationsMetric connectionMichael AtiyahMichael FreedmanMinimal Supersymmetric Standard ModelMinimal couplingModule (mathematics)Multilinear algebraMultivariable calculusNathan SeibergNeutrino oscillationNeutronNewtonian dynamicsNext-to-Minimal Supersymmetric Standard ModelNoether's theoremNoether chargeNon-Abelian groupNonlinear electrodynamicsNonlinear realizationNonlinear sigma modelNuclear physicsNumerical analysisNumerical linear algebraNumerical methods for ordinary differential equationsNumerical methods for partial differential equationsOperations researchOperator algebraOperator theoryOrdinary differential equationOrthogonal groupParity (physics)Partial derivativePartial differential equationParticle physicsParticle physics and representation theoryPartition function (quantum field theory)Path Integral FormulationPath integral formulationPaul FramptonPerturbation theoryPerturbation theory (quantum mechanics)Phase (waves)PhotonPhys. Rev.PhysicsPhysics beyond the Standard ModelPionPoincaré symmetryPoint (geometry)Poisson algebraPotential theoryPrincipal bundlePrincipal homogeneous spacePrinciple of general covariancePrinciple of least actionProbability amplitudeProbability distributionProbability theoryProca actionPropagator (Quantum Theory)ProtonQuantization (physics)QuantumQuantum chromodynamicsQuantum electrodynamicsQuantum field theoriesQuantum field theoryQuantum gravityQuantum groupQuantum mechanicsQuarkQuark modelQuarksRandom variableRegularization (physics)Relativistic quantum mechanicsRenormalizationRenormalization groupRobert Mills (physicist)Running couplingSU(3) × SU(2) × U(1)Scalar (mathematics)Scalar (physics)Scale (measurement)Scale anomalySchwinger-Dyson equationSean M. CarrollSection (fiber bundle)Seiberg–Witten invariantSimon DonaldsonSmooth functionSocial choice theorySociety for Industrial and Applied MathematicsSociété de Mathématiques Appliquées et IndustriellesSolid-state physicsSolverSpaceSpacetimeSpacetime algebraSpecial relativitySpecial unitary groupSpinorSplit supersymmetrySpontaneous symmetry breakingStandard ModelStandard Model (mathematical formulation)Statistical field theoryStatisticsStochastic calculusStochastic differential equationStochastic processString theoryStrong CP problemStrong forceStrong interactionStructure constantsStructure groupSudbury Neutrino ObservatorySuper-KamiokandeSuperalgebraSupercomputingSuperfluid vacuum theorySupergravitySuperstring theorySupersymmetric quantum mechanicsSupersymmetric theory of stochastic dynamicsSupersymmetrySupersymmetry algebraSymmetry (physics)Symmetry breakingSymmetry groupSymmetry in physicsSymmetry in quantum mechanicsT-symmetryTaylor & FrancisTechnicolor (physics)TensorTensor calculusTensor softwareTevatronThe Unreasonable Effectiveness of Mathematics in the Natural SciencesTheory of everythingTopic outline of mathematicsTopological chargeTopological field theoryTopological string theoryTopologyTurbulenceTwistor theoryU(1)Unitary groupUniversity of Chicago PressUp toVacuum expectation valueVacuum stateValidated numericsVector (geometry)Vector bundleVector calculusVector fieldVector potentialVladimir FockWard identitiesWave functionWeak bosonWeak forceWeak hyperchargeWeak interactionWeak isospinWedge productWheeler–DeWitt equationWick's theoremWightman axiomsWiley-VCHWilson loopWolfgang PauliYang–MillsYang–Mills existence and mass gapYang–Mills theory

67 concepts already in your glossary