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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Dirac equation canonical | 19 |
| Dirac theory of the electron | 2 |
| Dirac equation in a magnetic field for relativistic particles | 1 |
| 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Dirac equation Description of subject: 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.
Referenced by (23)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Weyl equation in 1+1 dimensions
this entity surface form:
Dirac theory of the electron
this entity surface form:
Dirac theory of the electron
this entity surface form:
Dirac equation in a magnetic field for relativistic particles