Dirac Lagrangian
E118073
The Dirac Lagrangian is the relativistic quantum field theory Lagrangian density that describes spin-½ fermions, such as electrons, and leads to the Dirac equation as their equation of motion.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Dirac Lagrangian canonical | 2 |
| Dirac Lagrangian density | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1006235 — 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 Lagrangian Context triple: [Dirac equation, relatedTo, Dirac Lagrangian]
-
A.
Dirac equation
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.
-
B.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
-
C.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
-
D.
LSZ reduction formula
The LSZ reduction formula is a key result in quantum field theory that relates time-ordered correlation functions of fields to observable scattering amplitudes in the S-matrix.
-
E.
Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
- 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 Lagrangian Target entity description: The Dirac Lagrangian is the relativistic quantum field theory Lagrangian density that describes spin-½ fermions, such as electrons, and leads to the Dirac equation as their equation of motion.
-
A.
Dirac equation
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.
-
B.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
-
C.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
-
D.
LSZ reduction formula
The LSZ reduction formula is a key result in quantum field theory that relates time-ordered correlation functions of fields to observable scattering amplitudes in the S-matrix.
-
E.
Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Lagrangian density
ⓘ
fermionic Lagrangian ⓘ relativistic quantum field theory Lagrangian ⓘ |
| appearsIn |
QED Lagrangian
ⓘ
linked to:
quantum electrodynamics
quark sector of the Standard Model ⓘ |
| associatedWithConservedCharge | electric charge (for charged fermions) ⓘ |
| basisFor |
Dirac propagator
ⓘ
linked to:
Feynman propagator
Feynman rules for fermion lines ⓘ |
| canBreak | chiral symmetry via mass term ⓘ |
| constructedBy | Paul Dirac ⓘ |
| couplesTo | electromagnetic field via minimal coupling ⓘ |
| decomposableInto | left-handed and right-handed chiral components ⓘ |
| definedOn |
Minkowski spacetime
ⓘ
linked to:
Minkowski space-time
|
| dependsOn |
Dirac adjoint spinor field ψ̄
ⓘ
Dirac spinor field ψ ⓘ fermion mass m ⓘ gamma matrices γ^μ ⓘ spacetime derivatives ∂_μ ⓘ |
| describes |
electrons
ⓘ
free fermion fields ⓘ positrons ⓘ spin-1/2 fermions ⓘ |
| equationOfMotionFor | Dirac field ⓘ |
| fieldType | spinor field theory ⓘ |
| gaugeCouplingForm | ℒ = ψ̄ (i γ^μ D_μ − m) ψ with D_μ = ∂_μ + i q A_μ ⓘ |
| generalizedTo |
curved spacetime via spin connection
ⓘ
gauge-covariant Dirac Lagrangian ⓘ |
| hasChiralLimit | massless Dirac Lagrangian with m = 0 ⓘ |
| hasForm | ℒ = ψ̄ (i γ^μ ∂_μ − m) ψ (in natural units) ⓘ |
| hasKineticTerm | ψ̄ i γ^μ ∂_μ ψ ⓘ |
| hasMassTerm | − m ψ̄ ψ ⓘ |
| impliesConservedCurrent | fermion number current ⓘ |
| introducedInContextOf | relativistic wave equation for the electron ⓘ |
| isInvariantUnder | global U(1) phase transformations of ψ ⓘ |
| isLorentz | Lorentz invariant ⓘ |
| leadsToConjugateMomentum | π = ∂ℒ/∂(∂_0 ψ) = i ψ̄ γ^0 ⓘ |
| obeys | Fermi–Dirac statistics ⓘ |
| relatedTo | Klein–Gordon Lagrangian via squaring the Dirac operator ⓘ |
| respects | CPT symmetry ⓘ |
| satisfies | Euler–Lagrange equations for fields ⓘ |
| usedIn |
Standard Model of particle physics
ⓘ
linked to:
Standard Model
particle physics ⓘ quantum field theory ⓘ relativistic quantum mechanics ⓘ |
| usedToConstruct | Hamiltonian density for Dirac fields ⓘ |
| usedToQuantize | fermionic fields via canonical quantization ⓘ |
| usesMetricSignature | Lorentzian metric ⓘ |
| yields | Dirac equation ⓘ |
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 Lagrangian Description of subject: The Dirac Lagrangian is the relativistic quantum field theory Lagrangian density that describes spin-½ fermions, such as electrons, and leads to the Dirac equation as their equation of motion.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Dirac Lagrangian
linked to: Dirac Lagrangian