Gseryakov

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 $\alpha$ 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)