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

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Discussion Overview

The discussion revolves around the nature of the symmetries U(1), SU(2), and SU(3) within the context of the Standard Model of particle physics. Participants explore whether these symmetries pertain to the action integral or the background spacetime, and whether they are expected to persist in General Relativity (GR) as well as Special Relativity (SR).

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that U(1), SU(2), and SU(3) are symmetries of the action or Lagrangian, not of spacetime.
  • Others emphasize that these symmetries are gauge symmetries that do not relate to the underlying spacetime.
  • A question is raised about the existence of a diffeomorphic invariant version of the path integral for particle physics that incorporates these symmetry groups.
  • One participant suggests that the Lagrangian remains unchanged if one replaces the Minkowski metric with the metric of curved spacetime.

Areas of Agreement / Disagreement

Participants generally agree that U(1), SU(2), and SU(3) are symmetries of the action and not of spacetime. However, there is ongoing debate regarding the implications of these symmetries in the context of GR and SR, as well as the existence of a diffeomorphic invariant path integral.

Contextual Notes

The discussion does not resolve the question of whether a diffeomorphic invariant version of the path integral exists, nor does it clarify the implications of these symmetries in different gravitational frameworks.

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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.
 
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They are symmetries of the action, or equivalently, the Lagrangian. They are not symmetries of spacetime.
 
Fredrik said:
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?
 
Yes, they are gauge symmetries that have nothing to do with the underlying spacetime.
 
Ben Niehoff said:
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?
 
friend said:
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}.
 

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