Dirac current
E504368
Dirac current is the conserved four-current associated with the global U(1) symmetry of the Dirac field, representing the flow of probability (or charge) for relativistic spin-½ particles.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Noether current
ⓘ
conserved current ⓘ four-current ⓘ physical quantity ⓘ |
| appearsInInteractionTerm | e \bar{ψ} γ^μ ψ A_μ ⓘ |
| associatedWith |
Dirac field
NERFINISHED
ⓘ
charge conservation ⓘ global U(1) symmetry ⓘ probability conservation ⓘ quantum field theory NERFINISHED ⓘ relativistic quantum mechanics ⓘ |
| conservedQuantityCorrespondsTo |
total electric charge
ⓘ
total probability ⓘ |
| couplesTo | electromagnetic four-potential A_μ ⓘ |
| definedFor |
fermions
ⓘ
spin-1/2 particles ⓘ |
| definedIn | Minkowski spacetime NERFINISHED ⓘ |
| derivedFrom | Dirac Lagrangian density NERFINISHED ⓘ |
| hasAdjointField | \bar{ψ} = ψ^† γ^0 ⓘ |
| hasComponentType | four-vector field ⓘ |
| hasDimension | (length)^{-3} in natural units ⓘ |
| hasMathematicalExpression | j^μ = \bar{ψ} γ^μ ψ ⓘ |
| hasSignProperty | time component j^0 is positive definite for physical states ⓘ |
| hasSpatialComponents | \vec{j} = ψ^† \vec{α} ψ ⓘ |
| hasTimeComponent | j^0 = ψ^† ψ ⓘ |
| integralOfTimeComponentGives |
total charge (with appropriate coupling)
ⓘ
total probability ⓘ |
| isBilinearIn | Dirac spinor field ψ ⓘ |
| isClassifiedAs | vector bilinear covariant of the Dirac field ⓘ |
| isConservedDueTo |
Noether theorem
NERFINISHED
ⓘ
global U(1) phase invariance of the Dirac Lagrangian ⓘ |
| isConservedOnShell | when Dirac equation is satisfied ⓘ |
| isGaugeInvariantUnder | global U(1) transformations ⓘ |
| isLocal | true ⓘ |
| isLorentzCovariant | true ⓘ |
| relatedConcept |
Dirac adjoint
NERFINISHED
ⓘ
continuity equation in field theory ⓘ probability density in relativistic quantum mechanics ⓘ |
| relatedTo | Dirac equation NERFINISHED ⓘ |
| represents |
electric charge current density
ⓘ
probability current density ⓘ |
| satisfiesEquation | ∂_μ j^μ = 0 ⓘ |
| transformsAs | four-vector under Lorentz transformations ⓘ |
| usedIn |
covariant formulation of probability current
ⓘ
electromagnetic interaction of Dirac fields ⓘ relativistic scattering theory ⓘ |
| usesMatrix |
α^i (Dirac alpha matrices)
ⓘ
γ^μ (gamma matrices) ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.