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 |
How this entity was disambiguated
This entity first appeared as the object of triple T173578 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirac equation Context triple: [Feynman checkerboard model, relatedTo, Dirac equation]
-
A.
Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
-
B.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
C.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
D.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
E.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Dirac equation Target entity description: 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.
-
A.
Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
-
B.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
C.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
D.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
E.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
- F. None of above. chosen
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 spacetime
ⓘ
linked to:
Minkowski space-time
|
| describes |
electrons
ⓘ
positrons ⓘ spin-1/2 particles ⓘ |
| dimensionOfSpinor | 4 ⓘ |
| explains | fine structure of hydrogen atom ⓘ |
| extends |
Schrödinger equation
ⓘ
linked to:
Tomonaga–Schwinger 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
ⓘ
Dirac operator ⓘ
linked to:
Atiyah–Singer index theorem
Dirac sea ⓘ |
| representation | 4-component spinor ⓘ |
| requires | Clifford algebra structure ⓘ |
| satisfies |
Lorentz invariance
ⓘ
principle of special relativity ⓘ |
| typeOf | spinor equation ⓘ |
| usedIn |
Standard Model of particle physics
ⓘ
linked to:
Standard Model
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.
linked to: Dirac equation
linked to: Dirac equation
linked to: Dirac equation
linked to: Dirac equation