Dirac adjoint field

E504367

Dirac spinor construction quantum field theory concept spinor field

The Dirac adjoint field is the spinor field obtained by taking the Hermitian conjugate of a Dirac spinor and multiplying by gamma^0, used to construct Lorentz-invariant bilinear quantities in relativistic quantum field theory.

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Observed surface forms (1)

Surface form	Occurrences
Dirac adjoint	1

Statements (47)

Predicate	Object
instanceOf	Dirac spinor construction ⓘ quantum field theory concept ⓘ spinor field ⓘ
alsoKnownAs	Dirac adjoint NERFINISHED ⓘ adjoint spinor field ⓘ
appearsIn	Dirac Lagrangian density NERFINISHED ⓘ Yukawa interaction terms ⓘ fermionic kinetic term \bar{\psi}(i\gamma^{\mu}\partial_{\mu}-m)\psi ⓘ gauge interaction terms \bar{\psi}\gamma^{\mu}A_{\mu}\psi ⓘ
constructedFrom	Dirac spinor field ⓘ Hermitian conjugate of Dirac spinor ⓘ gamma^0 matrix ⓘ
definedAs	\bar{\psi}(x) = \psi^{\dagger}(x) \gamma^{0} ⓘ
dependsOn	choice of gamma matrix representation ⓘ
domain	four-dimensional Minkowski spacetime ⓘ
ensures	Lorentz covariance of bilinear forms ⓘ Lorentz invariance of action integrals ⓘ
fieldType	fermionic field ⓘ
hasComponent	time-like gamma matrix \gamma^{0} ⓘ
hasOperation	Hermitian conjugation ⓘ
hasSpin	spin-1/2 ⓘ
introducedBy	Paul Dirac NERFINISHED ⓘ
invariantProperty	physical observables are representation independent ⓘ
mathematicalNature	complex-valued field ⓘ row spinor ⓘ
relatedEquation	Dirac equation NERFINISHED ⓘ
relatedTo	Dirac conjugation NERFINISHED ⓘ Dirac gamma matrices NERFINISHED ⓘ charge conjugation of spinor fields ⓘ
role	appears in conserved Noether currents for fermions ⓘ defines inner products in spinor space ⓘ defines probability current in Dirac theory ⓘ
symbol	\bar{\psi}(x) ⓘ
transformationProperty	ensures \bar{\psi}\gamma^{\mu}\psi is a Lorentz vector ⓘ ensures \bar{\psi}\psi is a Lorentz scalar ⓘ transforms covariantly under Lorentz transformations ⓘ
usedFor	construction of Lorentz-covariant interaction terms ⓘ
usedIn	Dirac theory of spin-1/2 particles ⓘ quantum electrodynamics ⓘ relativistic quantum field theory ⓘ
usedToConstruct	Dirac current NERFINISHED ⓘ Lorentz-invariant bilinears ⓘ axial vector bilinear \bar{\psi}\gamma^{\mu}\gamma^{5}\psi ⓘ pseudoscalar bilinear \bar{\psi} i\gamma^{5}\psi ⓘ scalar bilinear \bar{\psi}\psi ⓘ tensor bilinear \bar{\psi}\sigma^{\mu\nu}\psi ⓘ vector bilinear \bar{\psi}\gamma^{\mu}\psi ⓘ

Referenced by (2)

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

Dirac field → hasConjugateField → Dirac adjoint field ⓘ

Dirac spinors → innerProductDefinedBy → Dirac adjoint field ⓘ

this entity surface form: Dirac adjoint