A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

So, what we're talking about is something like a supersymmetric extension of the inhomogeneous gauge group analogous to supersymmetric extensions of the double cover of the inhomogeneous Lorentz or Poincaré group. Further, because this construction is at the level of groups, we've left a slot on the left-hand side on which to act. So, for example, if we want to take regular representations on the group, we can act by the group \(G\) on the left-hand side, because we're allowing the tilted gauge group to act on the right-hand side. So it's perfectly built for representation theory, and if you think back to Wigner's classification, and the concept that a particle should correspond to an irreducible representation of the inhomogeneous Lorentz group, we may be able to play the same games here, up to the issue of infinite-dimensionality.

Now, what would it mean to be able to use a gauge group in an intrinsic theory like this? We would be talking about something like an action, let's say a first-order action. And it would take the group \(G\), let's say to the real numbers, invariant, not under the full group, but under the tilted gauge subgroup.