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.

Aliases (4)

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 → classical mechanical systems → field theories → systems described by an action principle →
basedOn	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	first Noether theorem → 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 groups → Noether charge → Noether current → infinitesimal transformations →

Referenced by (7)

Subject (surface form when different)	Predicate
Noether's theorem ("first Noether theorem") → Noether's theorem ("second Noether theorem") →	hasVersion
Amalie Noether → Emmy Noether →	notableWork
Emmy Noether →	knownFor
Euler–Lagrange equation ("Noether’s theorem") →	relatedTo
Noether's theorem ("Noether current") →	usesConcept