Re: Actions, symmetries, and gauge theories

I guess the reason I'm interested in asking this is to find out whether
or not the symmetries of an action functional must necessarily be the
same as the symmetries of the resultant equations of motion for the
theory. As an extension, I wonder if the symmetries of an action could
generate a different symmetry group in the equations of motion.

The short answer is that the symmetries of a Lagrangian are always
symmetries
of the Euler-Lagrange equations. But there can be more symmetries of
the equations
than of the Lagrangian.

See for example, P. Olver, "Applications of Lie Groups to Differential
Equations".

charlie torre

.

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