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Summary The gauge-invariant renormalizable Lagrangian containing gauge kinetic terms, chiral fermion kinetic terms, one Higgs doublet, Yukawa couplings, and the Higgs potential.
Record metadata
Canonical name Standard Model Lagrangian
Concept ID standard_model_lagrangian
Content version 2.3.0
Alternate terminology No alternate terminology is currently authored for this record.
Concept type Theory formulation Incoming relations (arrows to this concept) Each relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID ewself_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation gauge kinetic interaction terms Authored explanation Triple and quartic electroweak gauge vertices arise from Standard Model gauge kinetic terms.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID fermionfield_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation chiral matter kinetic terms Authored explanation The Standard Model Lagrangian contains three generations of chiral fermion fields.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID covariantderivative_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation covariant kinetic terms Authored explanation Standard Model fermion and Higgs kinetic terms use the gauge-covariant derivative and thereby encode gauge interactions.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID fieldstrength_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation gauge kinetic terms Authored explanation The Standard Model Lagrangian contains field-strength kinetic terms for S U ( 3 ) C SU(3)_C S U ( 3 ) C , S U ( 2 ) L SU(2)_L S U ( 2 ) L , and U ( 1 ) Y U(1)_Y U ( 1 ) Y .
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID gaugeinteraction_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation covariant-derivative interactions Authored explanation Gauge interactions and field-strength terms are core Standard Model components.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID gluonfield_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation color gauge kinetic terms Authored explanation The Standard Model Lagrangian contains the S U ( 3 ) C SU(3)_C S U ( 3 ) C gluon field strength and quark color coupling.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID higgsdoublet_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation Higgs kinetic and potential terms Authored explanation The Higgs doublet and its potential are Standard Model components.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID higgsgauge_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation Higgs covariant-derivative terms Authored explanation Higgs–gauge interactions are explicit terms in the Standard Model Lagrangian.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID hyperfield_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation hypercharge gauge kinetic term Authored explanation The Standard Model Lagrangian contains the U ( 1 ) Y U(1)_Y U ( 1 ) Y hypercharge gauge field and its couplings.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID scalarself_to_higgs
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation Higgs potential Authored explanation The Higgs potential includes a quartic self-interaction.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID sm_to_chiral_multiplets
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation chiral fermion kinetic and gauge terms Authored explanation The Standard Model Lagrangian contains three generations of chiral fermion multiplets.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID smgroup_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation gauge invariance Authored explanation The Lagrangian is invariant under the local Standard Model gauge group before gauge fixing.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID weakfield_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation weak gauge kinetic terms Authored explanation The Standard Model Lagrangian contains the three S U ( 2 ) L SU(2)_L S U ( 2 ) L gauge fields and their non-Abelian field strength.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID yukawa_to_smlag
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation Yukawa matrices Authored explanation Yukawa couplings connect Higgs and fermion fields.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
Outgoing relations (arrows from this concept) Each relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Relation ID standard_model_lagrangian_to_standard_model_theory_component
Relation type Theory component theory-component
Direction source → target
Endpoint roles source: Contributes to; target: Contains theory component
Authored annotation encodes the local dynamics Authored explanation The Standard Model Lagrangian is the central local dynamical component encoding the theory’s fields, gauge symmetries, masses, and interactions.
How to interpret this relation type The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.