# What does it mean to say "internal symmetry"?

What does it mean to say "internal symmetry"? Let me try to express the way I see it, so you can have it as a starting point.

There are spacetime symmetries, which are global since any Lorentz transformation, at any point in spacetime, will be invariant. On the other hand there are also internal symmetries (which I understand as local), which are only invariant in a certain region of the spacetime.

1. Does this make sense?
2. Could anyone give examples of internal symmetries?

PS: I'm currently studying Classical Field Theory. That's where I see the terminology.

• Jun 19 '16 at 14:03

An internal symmetry is a transformation acting only on the fields, therefore not transforming spacetime points, and leaving the lagrangian or the physical results invariant. Example of internal symmetries are gauge symmetries. These are local symmetries, which means the transformations are in general spacetime dependent in the sense they are, in general, different for each spacetime point. Example: The $U(1)$ gauge symmetry of Maxwell theory and the $SU(3)$ color symmetry of quantum chromodynamics.