It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that these are not really symmetries because it means that there are only apparently different points in configuration space that are physically identical, but these are the same. I have a bunch of questions related to these considerations:
- Noether charge under the gauge symmetry is gauge dependent, so does this mean that only global symmetries make sense as symmetries?
- But why are local ones more fundamental?
- Under which conditions local symmetry implies the global one?
- Is conservation of electric charge due to local or global U(1) symmetry?
- Which symmetries are preferred by gravity, local or global?
- Is it general rule that some transformation is called symmetry if action is left invariant (classically)?
- Are there symmetries that strictly ask for Lagrangian to be left invariant?
- Are non-abelian symmetries "more" symmetries or redundancies in comparing to U(1)?
Which sentences I wrote here are wrong, or which questions are not valid?