A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
Revision as of 22:35, 15 April 2020
, 15 April 2020→Part II: Unified Field Content
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<p>[01:29:47] Now, just as in the finite dimensional case, we have a linear and a nonlinear component, right? Because at the topological level, this is just a Cartesian product. So if we wished to take products of fermions; of spinorial fields. We have a place to accept them. We can't figure out necessarily how to map them into the nonlinear sector, but we don't want to. | <p>[01:29:47] Now, just as in the finite dimensional case, we have a linear and a nonlinear component, right? Because at the topological level, this is just a Cartesian product. So if we wished to take products of fermions; of spinorial fields. We have a place to accept them. We can't figure out necessarily how to map them into the nonlinear sector, but we don't want to. | ||
<p>[01:30:09] So just the way, when we look at supersymmetry, we can take products of the spin-1/2 fields and map them into the linear sector. We can do the same thing here. 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. | <p>[01:30:09] So just the way, when we look at supersymmetry, we can take products of the spin-1/2 fields and map them into the linear sector. We can do the same thing here. 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. | ||
<p>[01:30:56] 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 dimentionality. | <p>[01:30:56] 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 dimentionality. | ||