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.

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AI-generated illustration of Dirac equation

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Prompt

Generate an image of the 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.)

All labels observed (4)

How this entity was disambiguated

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 ⓘ
describes electrons ⓘ
positrons ⓘ
spin-1/2 particles ⓘ
dimensionOfSpinor 4 ⓘ
explains fine structure of hydrogen atom ⓘ
extends 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 ⓘ
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 of particle physics ⓘ
linked to: Standard Model

quantum electrodynamics ⓘ
uses Dirac matrices ⓘ
Dirac spinors ⓘ
gamma matrices ⓘ
yearProposed 1928 ⓘ

How these facts were elicited

Referenced by (35)

Full triples — surface form annotated when it differs from this entity's canonical label.

Feynman checkerboard model → relatedTo → Dirac equation ⓘ
Feynman checkerboard model → relatedTo → Weyl equation in 1+1 dimensions ⓘ
linked to: Dirac equation
reduced Planck constant → appearsIn → Dirac equation ⓘ
Lorentz group → relatedTo → Dirac equation ⓘ
quantum electrodynamics → formulatedWith → Dirac equation ⓘ
quantum electrodynamics → historicalPrecursor → Dirac theory of the electron ⓘ
linked to: Dirac equation
Paul Dirac → notableWork → Dirac equation ⓘ
Klein–Nishina formula → basedOn → Dirac theory of the electron ⓘ
linked to: Dirac equation
Fermion → isDescribedBy → Dirac equation ⓘ
Klein–Gordon equation → precedes → Dirac equation ⓘ
Dirac matrices → usedIn → Dirac equation ⓘ
Dirac sea → basedOn → Dirac equation ⓘ
Dirac Lagrangian → yields → Dirac equation ⓘ
Dirac field → satisfies → Dirac equation ⓘ
Pauli equation → relatedTo → Dirac equation ⓘ
Dirac spinors → usedIn → Dirac equation ⓘ
Dirac spinors → satisfies → Dirac equation ⓘ
ħ → appearsIn → Dirac equation ⓘ
subject linked to: h-bar
Schrödinger equation → relatedTo → Dirac equation ⓘ
Planck units → simplifiesEquation → Dirac equation ⓘ
Landau levels → areSolutionOf → Dirac equation in a magnetic field for relativistic particles ⓘ
linked to: Dirac equation
Dirac operator → generalizes → Dirac equation ⓘ
Electron → isDescribedBy → Dirac equation ⓘ
Klein paradox → describedBy → Dirac equation ⓘ
Advanced Quantum Mechanics → topic → Dirac equation ⓘ
subject linked to: "Advanced Quantum Mechanics"
Dirac adjoint field → relatedEquation → Dirac equation ⓘ
Dirac current → relatedTo → Dirac equation ⓘ
Proca equation → relatedTo → Dirac equation ⓘ
Dirac Hamiltonian → basedOn → Dirac equation ⓘ
four-momentum operator → usedIn → Dirac equation ⓘ
The Positive Electron → relatedConcept → Dirac equation ⓘ
subject linked to: The Positive Electron (paper)
Clifford algebra → usedFor → Dirac equation ⓘ
Clifford analysis → isRelatedTo → Dirac equation ⓘ