Quote by bapowell
U(1), and gauge symmetries in general, are considered internal symmetries because the transformations are not occurring in spacetime. The symmetries correspond to internal "charges" (the charges are those quantities in the theory that are conserved under the symmetry transformations.) For example, the action of U(1) is to impart a phase shift to the wavefunction (or particle). Saying that two particles that differ by a phase shift are actually the same results in the existence of the electric charge. Mathematically, the theory describing the electromagnetic interaction is invariant under U(1) operations. This is an internal symmetry because there are no spacetime operations (like rotations or translations) that can change the phase of the wavefunction.

How about SU(3), SU(5)? Are they all internal symmetry?