The discussion centers on the invariance of equations of motion under gauge transformations, exploring whether they maintain this property across different theories, including electrodynamics and Yang-Mills theories. The scope includes theoretical considerations and mathematical proofs related to gauge invariance and covariance.
Participants express disagreement regarding the invariance of equations of motion under gauge transformations, with some asserting invariance and others maintaining that they are only covariant. No consensus is reached on this issue.
The discussion highlights the distinction between invariance and covariance, particularly in the context of different physical theories, but does not resolve the implications of these terms in specific cases.
Thanks!Demystifier said: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.