Noether's theorem

E29375

result in mathematics result in theoretical physics theorem

Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.

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All labels observed (8)

Label	Occurrences
Noether's theorem canonical	9
Noether’s theorem	8
Noether theorem	2
first Noether theorem	2
second Noether theorem	2
Noether current	1
Noether symmetry	1
Noether’s theorem formulations	1

How this entity was disambiguated

This entity first appeared as the object of triple T228991 — 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: Noether's theorem
Context triple: [Emmy Noether, notableWork, Noether's theorem]

A. 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.
B. 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.
C. equivalence principle
The equivalence principle is the foundational idea in relativity that locally, the effects of gravity are indistinguishable from those of acceleration, unifying gravitational and inertial mass.
D. 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.
E. 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.
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: Noether's theorem
Target entity description: Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.

A. 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.
B. 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.
C. equivalence principle
The equivalence principle is the foundational idea in relativity that locally, the effects of gravity are indistinguishable from those of acceleration, unifying gravitational and inertial mass.
D. 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.
E. 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.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	result in mathematics ⓘ result in theoretical physics ⓘ theorem ⓘ
appliesIn	Hamiltonian and Lagrangian formulations of mechanics ⓘ gauge theories ⓘ general relativity ⓘ particle physics ⓘ
appliesTo	Lagrangian systems ⓘ linked to: Lagrangian mechanics classical mechanical systems ⓘ field theories ⓘ systems described by an action principle ⓘ
basedOn	Euler–Lagrange equations ⓘ linked to: Euler–Lagrange equation calculus of variations ⓘ
concerns	invariance of the action under continuous transformations ⓘ symmetry groups of the action ⓘ
field	Lagrangian mechanics ⓘ classical field theory ⓘ differential geometry ⓘ mathematical physics ⓘ quantum field theory ⓘ symplectic geometry ⓘ theoretical physics ⓘ variational calculus ⓘ
hasConsequence	deep link between symmetry and conservation ⓘ systematic derivation of conservation laws ⓘ
hasDomain	continuous symmetries ⓘ differentiable manifolds ⓘ
hasVersion	first Noether theorem ⓘ linked to: Noether's theorem second Noether theorem ⓘ linked to: Noether's theorem
implies	conservation of angular momentum from rotational symmetry ⓘ conservation of electric charge from global gauge symmetry ⓘ conservation of energy from time-translation symmetry ⓘ conservation of linear momentum from spatial-translation symmetry ⓘ existence of a conserved current for each continuous symmetry ⓘ existence of a conserved quantity for each one-parameter Lie group of symmetries ⓘ
introducedIn	1918 ⓘ
isConsidered	fundamental principle of modern theoretical physics ⓘ
isFoundationFor	modern gauge theory ⓘ standard model of particle physics ⓘ
languageOfOriginalPublication	German ⓘ
namedAfter	Emmy Noether ⓘ
publishedIn	"Invariante Variationsprobleme" ⓘ
relates	conservation laws ⓘ continuous symmetries ⓘ
usesConcept	Lie groups ⓘ linked to: Lie group Noether charge ⓘ Noether current ⓘ linked to: Noether's theorem infinitesimal transformations ⓘ

How these facts were elicited

Referenced by (26)

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

Emmy Noether → notableWork → Noether's theorem ⓘ

Emmy Noether → knownFor → Noether's theorem ⓘ

subject linked to: Emmy

Noether's theorem → hasVersion → first Noether theorem ⓘ

linked to: Noether's theorem

Noether's theorem → hasVersion → second Noether theorem ⓘ

linked to: Noether's theorem

Noether's theorem → usesConcept → Noether current ⓘ

linked to: Noether's theorem

Amalie Noether → notableWork → Noether's theorem ⓘ

subject linked to: Amalie

Euler–Lagrange equation → relatedTo → Noether’s theorem ⓘ

linked to: Noether's theorem

Lagrangian mechanics → usesConcept → Noether's theorem ⓘ

Invariante Variationsprobleme → contains → first Noether theorem ⓘ

subject linked to: "Invariante Variationsprobleme"

linked to: Noether's theorem

Invariante Variationsprobleme → contains → second Noether theorem ⓘ

subject linked to: "Invariante Variationsprobleme"

linked to: Noether's theorem

Invariante Variationsprobleme → relatedConcept → Noether symmetry ⓘ

subject linked to: "Invariante Variationsprobleme"

linked to: Noether's theorem

Noether charge → basedOn → Noether's theorem ⓘ

Geometrical Methods of Mathematical Physics → topic → Noether’s theorem ⓘ

subject linked to: textbook "Geometrical Methods of Mathematical Physics"

linked to: Noether's theorem

Geometrical Methods of Mathematical Physics → hasSubject → Noether's theorem ⓘ

Hamiltonian mechanics → relatedConcept → Noether’s theorem ⓘ

linked to: Noether's theorem

First Law of Thermodynamics → relatedTo → Noether’s theorem ⓘ

linked to: Noether's theorem

stress–energy tensor → relatedTo → Noether theorem ⓘ

linked to: Noether's theorem

Invariance Principles and Elementary Particles → mainSubject → Noether’s theorem ⓘ

subject linked to: textbook "Invariance Principles and Elementary Particles"

linked to: Noether's theorem

Invariance Principles and Elementary Particles → mainSubject → Noether’s theorem ⓘ

subject linked to: "Invariance Principles and Elementary Particles"

linked to: Noether's theorem

mathematical foundations of mechanics → formalismIncludes → Noether's theorem ⓘ

Dirac current → isConservedDueTo → Noether theorem ⓘ

linked to: Noether's theorem

Liouville–Arnold theorem → relatedTo → Noether's theorem ⓘ

Ward–Takahashi identities → relatesTo → Noether’s theorem ⓘ

linked to: Noether's theorem

gauge theory → relatedTo → Noether's theorem ⓘ

four-momentum operator → usedIn → Noether’s theorem formulations ⓘ

linked to: Noether's theorem

Mathematical Methods of Classical Mechanics → topic → Noether’s theorem ⓘ

linked to: Noether's theorem

All labels observed (8)

How this entity was disambiguated Show

Statements (48)

How these facts were elicited Show

Referenced by (26)

How this entity was disambiguated

How these facts were elicited