Graduate Are equations of motion invariant under gauge transformations?

[Baela]

We know that all actions are invariant under their gauge transformations. Are the equations of motion also invariant under the gauge transformations?

If yes, can you show a mathematical proof (instead of just saying in words)?

 

[Dale]

Yes. Since the action is the same the path of least action is also the same.

 

[Demystifier]

No, in general they are just covariant. For electrodynamics the equations of motion are invariant under gauge transformations, but for Yang-Mills theories they are just covariant. Similarly, the Einstein-Hilbert action is invariant under general coordinate transformations, but the Einstein equation of motion is just covariant.

 

[Baela]

No, in general they are just covariant. For electrodynamics the equations of motion are invariant under gauge transformations, but for Yang-Mills theories they are just covariant. Similarly, the Einstein-Hilbert action is invariant under general coordinate transformations, but the Einstein equation of motion is just covariant.

Thanks!