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 18:52, 25 April 2020
, 25 April 2020→GU III: Physics
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===== GU III: Physics ===== | ===== GU III: Physics ===== | ||
<p>[01:43:06] Okay. We're not doing physics yet. We're just building tools. We've built ourselves a little bit of freedom. We have some reprieves. We've still got some very big debts to pay back for this magic beans trade. We're in the wrong dimension. We don't have good field content. We're stuck on this one spinor. We've built ourselves an projection operators. We've picked up some symmetric, nonlinear Sigma field. | <p>[01:43:06] Okay. We're not doing physics yet. We're just building tools. We've built ourselves a little bit of freedom. We have some reprieves. We've still got some very big debts to pay back for this magic beans trade. We're in the wrong dimension. We don't have good field content. We're stuck on this one spinor. We've built ourselves an projection operators. We've picked up some symmetric, nonlinear $$\Sigma$$ field. | ||
<p>[01:43:33] What can we write down in terms of equations of motion. Let's start with Einstein's concept. If we do Shiab of the curvature tensor of the gauge potential hit with an operator defined by the $$\epsilon$$-sigma field plus the star operator acting on the augmented torsion of the pair. This contains all of the information when $$\pi$$ is zero in Einstein's tensor. | <p>[01:43:33] What can we write down in terms of equations of motion. Let's start with Einstein's concept. If we do Shiab of the curvature tensor of the gauge potential hit with an operator defined by the $$\epsilon$$-sigma field plus the star operator acting on the augmented torsion of the pair. This contains all of the information when $$\pi$$ is zero in Einstein's tensor. | ||
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<p>[01:48:26] We'd now like to come up with a second operator here. This second operator here should have the property that the complex should be exact and the obstruction to it being a true complex -- to nilpotency -- should be exactly the generalization of the Einstein equations. Thus, unifying the spinorial matter with the intrinsic replacement for the curvature equations. | <p>[01:48:26] We'd now like to come up with a second operator here. This second operator here should have the property that the complex should be exact and the obstruction to it being a true complex -- to nilpotency -- should be exactly the generalization of the Einstein equations. Thus, unifying the spinorial matter with the intrinsic replacement for the curvature equations. | ||
<p>[01:48:59] Well, we know that $d_A$ composed with itself is going to be the curvature. And we know that we want that to be hit by a Shiab operator. And Shiab is a derivation, you can start to see that that's going to be curvature, so you want something like $$F_A$$ followed by Shiab over here to cancel. Then you think, okay, how am I going to get at getting this augmented torsion? | <p>[01:48:59] Well, we know that $$d_A$$ composed with itself is going to be the curvature. And we know that we want that to be hit by a Shiab operator. And Shiab is a derivation, you can start to see that that's going to be curvature, so you want something like $$F_A$$ followed by Shiab over here to cancel. Then you think, okay, how am I going to get at getting this augmented torsion? | ||
<p>[01:49:32] And, then you realize that the information in the inhomogeneous gauge group, you actually have information not for one connection, but for two connections. | <p>[01:49:32] And, then you realize that the information in the inhomogeneous gauge group, you actually have information not for one connection, but for two connections. | ||