# U(1), SU(2), SU(3) are symmetry of what?

1. Feb 11, 2012

### friend

The Standard Model symmetries are U(1), SU(2), and SU(3). But I'm not sure whether these are symmetries of the Action intgral or if they are symmetries of the background spacetime.

2. Feb 11, 2012

### Fredrik

Staff Emeritus
They are symmetries of the action, or equivalently, the Lagrangian. They are not symmetries of spacetime.

3. Feb 11, 2012

### friend

Are these symmetries expected to survive in GR as well as in SR?

4. Feb 11, 2012

### Ben Niehoff

Yes, they are gauge symmetries that have nothing to do with the underlying spacetime.

5. Feb 11, 2012

### friend

So is there a diffeomorphic invariant version of the path integral for particle physics that uses the U(1), SU(2), and SU(3) symmetry groups?

6. Feb 12, 2012

### Ben Niehoff

The Lagrangian is exactly the same; just replace $\eta_{\mu\nu}$ with $g_{\mu\nu}$.