My understanding of a symmetry is this: apply an operation (e. g. parity inversion) to a system. If it behaves the same afterwards, it is symmetric under that operation.
Now, quite often I see statements like this:
Isospin is regarded as a symmetry of the strong interaction under the action of the Lie group SU(2), the two states being the up flavour and down flavour. [...] In simple terms, [the] energy operator for the strong interaction gives the same result when an up quark and an otherwise identical down quark are swapped around.
- How can the strong interaction "have a symmetry"? An interaction is not a one-time operation like parity inversion. Is the meaning of this that any strong interacting process does not affect the isospin? Or that reversal of all isospins in a system does not change the behavior of the strong interaction?
- I also don't see how in the specific example from above a down quark is suddenly "otherwise identical" to an up quark except for its isospin. Wouldn't up and down quarks always differ by mass and electric charge?