SU(2)_L

E12518

SU(2)_L is the non-Abelian weak isospin gauge symmetry of the Standard Model that governs left-handed weak interactions.

Aliases (1)

Statements (49)
Predicate Object
instanceOf Lie group
gauge symmetry
non-Abelian gauge group
weak isospin symmetry
actsOn left-handed fermions
left-handed lepton doublets
left-handed quark doublets
algebra su(2)
appearsIn Standard Model Lagrangian
associatedGaugeBosons W^1
W^2
W^3
associatedQuantumNumber weak isospin
breaksAtEnergyScale electroweak scale (~246 GeV)
chirality left-handed
commutationRelations [T^a, T^b] = i ε^{abc} T^c
covariantDerivativeContribution - i g T^a W^a_μ
dimension 3
doesNotActOn right-handed charged leptons
right-handed down-type quarks
right-handed fermions (in the minimal Standard Model)
right-handed up-type quarks
fundamentalRepresentation weak isospin doublet
fundamentalRepresentationDimension 2
gaugeBosonsAfterSymmetryBreaking W^+
W^-
Z boson (in combination with U(1)_Y)
gaugeCoupling g
gaugeFields W^a_μ (a = 1,2,3)
gaugeGroupFactorOf SU(3)_C × SU(2)_L × U(1)_Y
gaugeGroupOf weak interaction
generators three
globalVersion isospin SU(2) (in nuclear physics, distinct but related)
interactionType part of weak neutral current (via mixing)
weak charged current
isNonAbelian true
localSymmetry yes
mediates flavor-changing weak processes
partOf electroweak sector of the Standard Model
preserves CPT symmetry
rank 1
relatedMixingAngle Weinberg angle θ_W
relatedToElectricChargeBy Q = T_3 + Y/2
spontaneouslyBrokenBy Higgs field vacuum expectation value
structureConstants Levi-Civita symbol ε^{abc}
thirdComponentGenerator T_3
unbrokenSubgroupAfterEWSB U(1)_em
violates charge conjugation symmetry
parity symmetry

Referenced by (3)
Subject (surface form when different) Predicate
Salam–Weinberg model
hasGaugeGroup
W boson
isGaugeBosonOf
Higgs field ("SU(2)_L gauge group")
transformsUnder

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