Re: Actions, symmetries, and gauge theories


A symmetry of the action functional implies a symmetry of the equations
of motion (Noether's theorem). But, a priori, the reverse need not be
true. However, I'm not sure I can provide an example off the top of my
head.

A standard example is to consider a Lagrangian which yields linear
Euler-Lagrange equations. The equations, being linear, admit a
scaling symmetry. The Lagrangian typically will not admit that
symmetry.

charlie

.