Pauli–Lubanski pseudovector

E646032

Poincaré group invariant pseudovector quantum mechanical operator

The Pauli–Lubanski pseudovector is a relativistic quantum-mechanical operator that encodes a particle’s intrinsic spin and serves as the generator of internal angular momentum in representations of the Poincaré group.

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Observed surface forms (1)

Surface form	Occurrences
Pauli–Lubanski vector	1

Statements (45)

Predicate	Object
instanceOf	Poincaré group invariant ⓘ pseudovector ⓘ quantum mechanical operator ⓘ
appearsIn	Dirac theory of spin-1/2 particles ⓘ Proca theory of spin-1 fields NERFINISHED ⓘ relativistic wave equations ⓘ
belongsTo	Poincaré group representation theory toolkit ⓘ
commutesWith	four-momentum operator in an irreducible representation ⓘ
componentCount	4 ⓘ
covarianceProperty	Lorentz covariant ⓘ
definedOn	Hilbert space of relativistic states ⓘ
dependsOn	four-momentum operator ⓘ total angular momentum operator ⓘ
distinguishes	different spin sectors of a given mass representation ⓘ
domain	states in relativistic quantum theories ⓘ
eigenvaluesInterpretation	spin of the particle ⓘ
encodes	intrinsic spin of a particle ⓘ
field	quantum field theory ⓘ relativistic quantum mechanics ⓘ representation theory of the Poincaré group ⓘ
hasComponent	Pauli–Lubanski 4-vector NERFINISHED ⓘ
hasSignatureDependence	depends on metric signature convention ⓘ
introducedInContext	relativistic description of spin ⓘ
invariantUnder	Poincaré group translations NERFINISHED ⓘ
isCasimirOf	Poincaré algebra NERFINISHED ⓘ
mathematicalNature	four-vector operator ⓘ
namedAfter	Józef Lubański NERFINISHED ⓘ Wolfgang Pauli NERFINISHED ⓘ
objectType	operator-valued 4-vector ⓘ
physicalMeaning	generator of internal rotations in the particle rest frame ⓘ
relatedConcept	Casimir invariants of the Poincaré group ⓘ helicity operator ⓘ spin 4-vector ⓘ
relatedTo	Lorentz generators NERFINISHED ⓘ total angular momentum tensor ⓘ
role	generator of internal angular momentum ⓘ
squaredOperator	Pauli–Lubanski scalar W^μ W_μ NERFINISHED ⓘ
squaredOperatorEigenvaluesInterpretation	spin Casimir invariant of the Poincaré group ⓘ
tensorRank	1 ⓘ
transformationProperty	transforms as an axial 4-vector under proper Lorentz transformations ⓘ
usedFor	defining helicity for massless particles ⓘ defining spin for massive particles ⓘ labeling irreducible unitary representations of the Poincaré group ⓘ
usedIn	Wigner classification NERFINISHED ⓘ classification of elementary particles ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

spin Casimir operator → definedInTermsOf → Pauli–Lubanski pseudovector ⓘ

spin Casimir operator → relatedConcept → Pauli–Lubanski pseudovector ⓘ

this entity surface form: Pauli–Lubanski vector