Dirac equation
E21718
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
Observed surface forms (2)
| Surface form | Occurrences |
|---|---|
| Dirac theory of the electron | 2 |
| Weyl equation in 1+1 dimensions | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
equation in quantum mechanics
ⓘ
fundamental equation of physics ⓘ relativistic wave equation ⓘ |
| appliesTo |
fermions
ⓘ
spinor fields ⓘ |
| category | equations of motion in quantum theory ⓘ |
| covariantForm | (i γ^μ ∂_μ − m) ψ = 0 ⓘ |
| definedOver |
Minkowski space-time
ⓘ
surface form:
Minkowski spacetime
|
| describes |
electrons
ⓘ
positrons ⓘ spin-1/2 particles ⓘ |
| dimensionOfSpinor | 4 ⓘ |
| explains | fine structure of hydrogen atom ⓘ |
| extends |
Tomonaga–Schwinger equation
ⓘ
surface form:
Schrödinger equation
|
| field |
particle physics
ⓘ
quantum field theory ⓘ quantum mechanics ⓘ theoretical physics ⓘ |
| framework | relativistic quantum mechanics ⓘ |
| generalizes | Klein–Gordon equation ⓘ |
| governs | free relativistic electron ⓘ |
| hasSolutionType |
negative-energy solutions
ⓘ
positive-energy solutions ⓘ |
| historicalSignificance | first theory to unify quantum mechanics and special relativity for electrons ⓘ |
| implies | spin–orbit coupling ⓘ |
| includes |
coupling to electromagnetic four-potential
ⓘ
mass term ⓘ |
| introducedBy | Paul Dirac ⓘ |
| mathematicalForm | first-order linear differential equation ⓘ |
| namedAfter | Paul Dirac ⓘ |
| nonRelativisticLimit | Pauli equation ⓘ |
| predicts |
antimatter
ⓘ
electron magnetic moment close to observed value ⓘ existence of the positron ⓘ |
| quantizesTo | Dirac field ⓘ |
| relatedTo |
Dirac Lagrangian
ⓘ
Atiyah–Singer index theorem ⓘ
surface form:
Dirac operator
Dirac sea ⓘ |
| representation | 4-component spinor ⓘ |
| requires | Clifford algebra structure ⓘ |
| satisfies |
Lorentz invariance
ⓘ
principle of special relativity ⓘ |
| typeOf | spinor equation ⓘ |
| usedIn |
Standard Model
ⓘ
surface form:
Standard Model of particle physics
quantum electrodynamics ⓘ |
| uses |
Dirac matrices
ⓘ
Dirac spinors ⓘ gamma matrices ⓘ |
| yearProposed | 1928 ⓘ |
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Dirac theory of the electron
this entity surface form:
Dirac theory of the electron
this entity surface form:
Weyl equation in 1+1 dimensions