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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]
Being Lagrangian symmetries, gauge symmetries of a Lagrangian satisfy Noether's first theorem, but the corresponding conserved current takes a particular superpotential form = + where the first term vanishes on solutions of the Euler–Lagrange equations and the second one is a boundary term, where is called a superpotential.
Noether identities need not be independent, but satisfy first-stage Noether identities, which are subject to the second-stage Noether identities and so on. Higher-stage Noether identities also are separated into the trivial and non-trivial once. A degenerate Lagrangian is called reducible if there exist non-trivial higher-stage Noether identities.
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)
The appellation of charge comes from the notion of charges in physics, which correspond to the generators of physical symmetries (via Noether's theorem). The perceived symmetry is that multiplication by a single Grassmann variable swaps the Z 2 {\displaystyle \mathbb {Z} _{2}} grading between fermions and bosons; this is discussed in greater ...
Herglotz–Noether theorem, in special relativity; Lasker–Noether theorem, that states that every Noetherian ring is a Lasker ring; Skolem–Noether theorem, which characterizes the automorphisms of simple rings; Albert–Brauer–Hasse–Noether theorem, in algebraic number theory; Brill–Noether theory, in the theory of algebraic curves
An application of the second isomorphism theorem identifies projective linear groups: for example, the group on the complex projective line starts with setting = (), the group of invertible 2 × 2 complex matrices, = (), the subgroup of determinant 1 matrices, and the normal subgroup of scalar matrices = {():}, we have = {}, where is ...
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 ...