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 (7)

Label	Occurrences
Noether's theorem canonical	6
Noether’s theorem	4
first Noether theorem	2
second Noether theorem	2
Noether current	1
Noether symmetry	1
Noether theorem	1

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 mechanics ⓘ surface form: Lagrangian systems classical mechanical systems ⓘ field theories ⓘ systems described by an action principle ⓘ
basedOn	Euler–Lagrange equation ⓘ surface form: Euler–Lagrange equations 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	Noether's theorem self-linksurface differs ⓘ surface form: first Noether theorem Noether's theorem self-linksurface differs ⓘ surface form: second Noether 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 group ⓘ surface form: Lie groups Noether charge ⓘ Noether's theorem self-linksurface differs ⓘ surface form: Noether current infinitesimal transformations ⓘ

Referenced by (17)

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

Emmy Noether → notableWork → Noether's theorem ⓘ

Emmy → knownFor → Noether's theorem ⓘ

subject surface form: Emmy Noether

Noether's theorem → hasVersion → Noether's theorem self-linksurface differs ⓘ

this entity surface form: first Noether theorem

Noether's theorem → hasVersion → Noether's theorem self-linksurface differs ⓘ

this entity surface form: second Noether theorem

Noether's theorem → usesConcept → Noether's theorem self-linksurface differs ⓘ

this entity surface form: Noether current

Amalie → notableWork → Noether's theorem ⓘ

subject surface form: Amalie Noether

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

this entity surface form: Noether’s theorem

Lagrangian mechanics → usesConcept → Noether's theorem ⓘ

"Invariante Variationsprobleme" → contains → Noether's theorem ⓘ

subject surface form: Invariante Variationsprobleme

this entity surface form: first Noether theorem

"Invariante Variationsprobleme" → contains → Noether's theorem ⓘ

subject surface form: Invariante Variationsprobleme

this entity surface form: second Noether theorem

"Invariante Variationsprobleme" → relatedConcept → Noether's theorem ⓘ

subject surface form: Invariante Variationsprobleme

this entity surface form: Noether symmetry

Noether charge → basedOn → Noether's theorem ⓘ

textbook "Geometrical Methods of Mathematical Physics" → topic → Noether's theorem ⓘ

subject surface form: Geometrical Methods of Mathematical Physics

this entity surface form: Noether’s theorem

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

Hamiltonian mechanics → relatedConcept → Noether's theorem ⓘ

this entity surface form: Noether’s theorem

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

this entity surface form: Noether’s theorem

stress–energy tensor → relatedTo → Noether's theorem ⓘ

this entity surface form: Noether theorem