# What is meant by "the symmetry of an interaction"?

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?
• In the case of isospin you can change a proton for a neutron and vice versa without affecting the result of the interaction. Would you not call this a "symmetry"? Sep 23, 2018 at 14:14
• Thanks, that makes sense! So it is meant that flipping all isospins does not change the behavior the strong interaction? As another example, would electric charge be a symmetry of the electromagnetic force? Conjugating all charges would still leave to electrons repelling each other etc.
– Fii
Sep 23, 2018 at 14:22
• The "otherwise identical" wording of the article is unfortunate, as I think it has mislead you in this case. Particles can (and usually are) symmetrical /invarient/indistinguisible in respect of some properties/operations, but by no means for all operations, is what should have been stressed.
– user207480
Sep 23, 2018 at 14:31