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Noether's theorem


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Every continuous symmetry under which the Lagrangian (or Hamiltonian) is invariant in form is associated with a conservation law. For example, invariance of a Langrangian under time displacement implies the conservation of energy. Not all conservation laws are associated with continuous symmetries, since some conservation laws are associated with topology, particularly for solitons. It does not automatically follow that if there is a conserved quantity in a classical field theory associated with Noether's theorem, there is a conserved quantity in the corresponding quantum field theory; this raises the possibility of an anomaly. Noether's theorem was stated in 1918 by the German mathematician Amalie Emmy Noether (1882–1935).

Subjects: Physics.


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