four-momentum operator
E646031
four-vector
generator of spacetime translations
observable
quantum mechanical operator
relativistic operator
The four-momentum operator is the relativistic quantum operator whose components generate spacetime translations, combining energy (via the Hamiltonian) and momentum into a single four-vector.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
four-vector
ⓘ
generator of spacetime translations ⓘ observable ⓘ quantum mechanical operator ⓘ relativistic operator ⓘ |
| actsOn |
Hilbert space
NERFINISHED
ⓘ
quantum fields ⓘ state vectors ⓘ |
| appearsIn |
Heisenberg equation of motion
NERFINISHED
ⓘ
S-matrix formulation NERFINISHED ⓘ propagators ⓘ |
| associatedWith | unitary representation of translations ⓘ |
| associatedWithSymmetry | spacetime translations ⓘ |
| commutesWith | itself at different components up to structure constants ⓘ |
| componentOf | Poincaré algebra NERFINISHED ⓘ |
| conservedQuantityCorrespondsTo |
energy
ⓘ
momentum ⓘ |
| constructedFrom | stress–energy tensor ⓘ |
| definedIn |
quantum field theory
NERFINISHED
ⓘ
relativistic quantum mechanics ⓘ |
| domainIncludes |
multi-particle Fock space
ⓘ
single-particle states ⓘ |
| eigenvaluesInclude |
energy
ⓘ
three-momentum ⓘ |
| eigenvaluesRepresent | four-momentum of particle ⓘ |
| frameTransformsAs | Lorentz four-vector NERFINISHED ⓘ |
| generates |
spatial translations
ⓘ
time translations ⓘ |
| hasComponent |
Hamiltonian operator
NERFINISHED
ⓘ
momentum operator ⓘ |
| hasDimension |
energy
ⓘ
momentum ⓘ |
| hasMetricSignature | Minkowski metric NERFINISHED ⓘ |
| hasSpatialComponent | three-momentum operator ⓘ |
| hasTimeComponent | energy operator ⓘ |
| mathematicalNature | self-adjoint operator (under suitable conditions) ⓘ |
| relatedTo |
Poincaré group
NERFINISHED
ⓘ
mass-shell condition ⓘ |
| role | unifies energy and momentum in relativistic quantum theory ⓘ |
| satisfies |
P^μ P_μ = m^2 for one-particle states (in units c=1)
ⓘ
Poincaré commutation relations NERFINISHED ⓘ |
| spatialComponentsProportionalTo | momentum operators ⓘ |
| symbol |
\hat P^μ
ⓘ
P^μ ⓘ |
| timeComponentProportionalTo | Hamiltonian NERFINISHED ⓘ |
| usedIn |
Dirac equation
NERFINISHED
ⓘ
Klein–Gordon equation NERFINISHED ⓘ Noether’s theorem formulations NERFINISHED ⓘ relativistic wave equations ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.