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 00:42, 14 April 2020
, 14 April 2020→Supplementary Explainer Presentation
| Line 733: | Line 733: | ||
<p>[02:23:52] So there is one way in which we've reversed the fundamental theorem of Riemannian in geometry where a connection on $$X$$ leads to a metric on $$Y$$. So if we do the full transmission mechanism out, a Gimmel on X leads to alpha sub Gimmel for the Levi-Civita connection on X. Alpha sub Gimmel live leads to a G sub alpha, which is, or sorry, the G sub Alef. | <p>[02:23:52] So there is one way in which we've reversed the fundamental theorem of Riemannian in geometry where a connection on $$X$$ leads to a metric on $$Y$$. So if we do the full transmission mechanism out, a Gimmel on X leads to alpha sub Gimmel for the Levi-Civita connection on X. Alpha sub Gimmel live leads to a G sub alpha, which is, or sorry, the G sub Alef. | ||
<p>[02:24:17] | <p>[02:24:17] I'm not used to using Hebrew in math. So G_aleph is a metric on $$Y$$ and that creates a Levi-Civita connection of the metric on the space $$Y$$ as well, which then induces one on the spinorial levels. In sector two, the inhomogenous gauge group on $$Y$$ replaces the Poincaré group and the internal symmetries that are found on $$X$$. | ||
<p>[02:24:50] And in fact, you use a fermionic extension of the inhomogeneous gauge group (IGG) to replace the supersymmetric Poincaré group, and that would be with the field content, zero forms, tensors and spinors, tensors with spinors, a direct sum one-forms tensor to spinors all up on $$Y$$ as the | <p>[02:24:50] And in fact, you use a fermionic extension of the inhomogeneous gauge group (IGG) to replace the supersymmetric Poincaré group, and that would be with the field content, zero forms, tensors and spinors, tensors with spinors, a direct sum one-forms tensor to spinors all up on $$Y$$ as the fermionic field content. | ||
<p>[02:25:09] So, that gets rid of the biggest problem because the internal symmetry group is what causes the failure, I think, of supersymmetric particles to be seen in nature, which is we have to have two different origin stories, which is a little bit like Lilith | <p>[02:25:09] So, that gets rid of the biggest problem because the internal symmetry group is what causes the failure, I think, of supersymmetric particles to be seen in nature, which is we have to have two different origin stories, which is a little bit like Lilith and Genesis. We can't easily say we have a unified theory. | ||
<p>[02:25:32] If spacetime and the SU(3) cross SU(2) cross U(1) group that lives on space-time have different origins and cannot be related. In this situation, we tie our hands and we have no choice over the group content. So just to fix bundle notation, we let H be the structure group of a bundle piece of H over a base space, B. | <p>[02:25:32] If spacetime and the SU(3) cross SU(2) cross U(1) group that lives on space-time have different origins and cannot be related. In this situation, we tie our hands and we have no choice over the group content. So, just to fix bundle notation, we let $$H$$ be the structure group of a bundle piece of $$H$$ over a base space, $$B$$. | ||
<p>[02:25:56] We use pi for the projection map. We've reserved the variation in the pi orthography. For the field content and we try to use right principal actions. I'm terrible with left and right, but we do our best. We use H here, not, G because we want to reserve G for the inhomogeneous extension of H, once we moved to function spaces. | <p>[02:25:56] We use $$\pi$$ for the projection map. We've reserved the variation in the pi orthography. For the field content and we try to use right principal actions. I'm terrible with left and right, but we do our best. We use $$H$$ here, not, $$G$$ because we want to reserve $$G$$ for the inhomogeneous extension of $$H$$, once we moved to function spaces. | ||
<p>[02:26:23] So, with function spaces, we can take the bundle of groups. Using the adjoint action of H on itself and form the associated bundle, and then move to C infinity sections to get the so-called gauge group of automorphisms. We have a space of connections, typically denoted by A, and we're going to promote a $$\Omega_1$$, a tensor in the adjoint bundle to a notation of. | <p>[02:26:23] So, with function spaces, we can take the bundle of groups. Using the adjoint action of $$H$$ on itself and form the associated bundle, and then move to C infinity sections to get the so-called gauge group of automorphisms. We have a space of connections, typically denoted by A, and we're going to promote a $$\Omega_1$$, a tensor in the adjoint bundle to a notation of. | ||
<p>[02:26:54] Script N a as the affine group, which acts directly on the space of connections. Now the inhomogeneous gauge group is formed as the semi-direct product of the gauge group of automorphisms together with the affine group of translations of the space of connections. And you can see here is a version of an explicit group multiplication rule. | <p>[02:26:54] Script N a as the affine group, which acts directly on the space of connections. Now the inhomogeneous gauge group is formed as the semi-direct product of the gauge group of automorphisms together with the affine group of translations of the space of connections. And you can see here is a version of an explicit group multiplication rule. | ||