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

[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.

 

[Fredrik]

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

 

[friend]

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

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

 

[Ben Niehoff]

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

 

[friend]

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

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?

 

[Ben Niehoff]

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?

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