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symmetries and conservation laws

May 14, 2011

One of the most beautiful results in modern physics is the connection between symmetry and conservation laws established by Emmy Noether near the beginning of the 20th century. The present paper served as a prelude to a discussion we had earlier this year about whether such results can be extended to dynamical systems that are more general than those normally considered in classical physics. After defining the Lagrangian formulation of classical mechanics and its transformations under a change in coordinates, it shows how conserved quantities arise from invariance under particular coordinate transformations. A later draft will extend this derivation to continuous (field) systems. PDF

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