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Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem ) published by mathematician Emmy Noether in 1918. [ 1 ]
Noether's work in abstract algebra and topology was influential in mathematics, while Noether's theorem has widespread consequences for theoretical physics and dynamical systems. Noether showed an acute propensity for abstract thought, which allowed her to approach problems of mathematics in fresh and original ways. [ 42 ]
In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. [1] It states that for any field k , and any finitely generated commutative k -algebra A , there exist elements y 1 , y 2 , ..., y d in A that are algebraically independent over k and such that A is a finitely generated module ...
Specifically, the theorem says that if the action has an infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by k arbitrary functions and their derivatives up to order m, then the functional derivatives of L satisfy a system of k differential equations. Noether's second theorem is sometimes used in gauge theory.
This is an accepted version of this page This is the latest accepted revision, reviewed on 6 February 2025. Law of physics and chemistry This article is about the law of conservation of energy in physics. For sustainable energy resources, see Energy conservation. Part of a series on Continuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion Laws ...
This is an instance of Noether's theorem. Here, the conserved quantity is the stress–energy tensor , which is only conserved on shell, that is, if the equations of motion are satisfied. References
Time-translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time-translation symmetry is closely connected, via Noether's theorem, to conservation of energy. [1] In mathematics, the set of all time translations on a given system form a Lie group.
No wandering domain theorem (ergodic theory) Noether's theorem (Lie groups, calculus of variations, differential invariants, physics) Noether's second theorem (calculus of variations, physics) Noether's theorem on rationality for surfaces (algebraic surfaces) Non-squeezing theorem (symplectic geometry) Norton's theorem (electrical networks)