Proca equation
E505996
The Proca equation is a relativistic wave equation that describes massive spin-1 fields, such as massive vector bosons, in quantum field theory.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
equation of motion
ⓘ
relativistic wave equation ⓘ |
| appliesTo |
massive vector fields
ⓘ
spin-1 particles ⓘ |
| assumes | flat Minkowski spacetime in its simplest form ⓘ |
| breaks | gauge invariance present in Maxwell theory ⓘ |
| category |
quantum field theory equations
ⓘ
relativistic wave equations ⓘ theoretical physics ⓘ |
| compatibleWith | special relativity NERFINISHED ⓘ |
| describes |
massive spin-1 fields
ⓘ
massive vector bosons ⓘ |
| describesParticleType |
W boson
NERFINISHED
ⓘ
Z boson NERFINISHED ⓘ massive vector boson ⓘ |
| expressedIn | covariant tensor notation ⓘ |
| extendedTo | curved spacetime in general relativity ⓘ |
| fieldType | four-vector field ⓘ |
| formulatedBy | Alexandre Proca NERFINISHED ⓘ |
| generalizes | Maxwell equations for massive photons ⓘ |
| governs | propagation of massive vector fields ⓘ |
| implies |
Lorenz condition for massive vector fields
ⓘ
three physical polarization states for massive spin-1 fields ⓘ |
| includesTerm | mass term for the vector field ⓘ |
| LagrangianDensityIncludes |
½ m^2 A_μ A^μ
ⓘ
−¼ F_{μν}F^{μν} ⓘ |
| mathematicalForm | (∂_μ∂^μ + m^2)A^ν − ∂^ν(∂_μ A^μ) = 0 ⓘ |
| namedAfter | Alexandre Proca NERFINISHED ⓘ |
| quantizationLeadsTo | massive spin-1 quantum field ⓘ |
| reducesTo | Maxwell equations in the zero-mass limit ⓘ |
| relatedTo |
Dirac equation
NERFINISHED
ⓘ
Klein–Gordon equation NERFINISHED ⓘ |
| requires | nonzero mass parameter ⓘ |
| spin | 1 ⓘ |
| usedFor | phenomenological description of massive photons ⓘ |
| usedIn |
effective field theories for massive vectors
ⓘ
massive electrodynamics ⓘ quantum field theory NERFINISHED ⓘ relativistic quantum mechanics ⓘ |
| usedToCompute | propagator of a massive vector field ⓘ |
| violates | local U(1) gauge invariance ⓘ |
| yearProposed | 1936 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.