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A nice way to describe physical systems is through the Lagrangian formalism. The dynamical equations of the formalisim take the form of a variational principle. Any infinitesimal symmetry transformation that leaves the action unchanged need not leave the variation of the action unchanged. In order that this must vanish when the change in the infinitesimal is constant we require that the fields to which we are applying our transformations obey a conservation law. Conservation laws come from symmetry, this is Noether's theorm. Examples:
  • Conservation of momentum -- from translational symmetry
  • Conservation of angular momentum -- from rotational symmetry
  • Conservation of energy -- from time symmetry <\ul>

    there are many conservation laws which come about from symmetry.

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