User talk:Gseryakov

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[edit] How integrals generate symmetry transformation

Gseryakov, might your addition to Noether's theorem,

viz. consider the conservating value as a new Hamiltonian; the evolution generated by this Hamiltonian will be the symmetry transformation

be also stated

consider the physical variables for the conserved current in a new Hamiltonian; the evolution generated by this Hamiltonian will be the symmetry transformation

Still true? Thank you Ancheta Wis 23:43, 9 May 2005 (UTC)


Not exactly. What I meant - Suppose we have a dynamical system with action principle
\int_{}^{} (pdq - Hdt) \to min
Suppose we have intergal I - conservating value. Then if we consider dynamical system defined with the action principle as
\int_{}^{} (pdq - Id\alpha) \to min
then the dynamics by α will give us the symmetry transformation corresponding to the integral I.
I can be thought as one logical step and should be expressed in one sentence.
--GS 01:35, 10 May 2005 (UTC)