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 18:02, 25 April 2020
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====== Unified Field Content Plus a Toolkit ====== | ====== Unified Field Content Plus a Toolkit ====== | ||
<p>[01:33:43] So we've, we've restricted ourselves to one gauge group, this big unitary group on the spinors using whatever sort of inner product naturally exists on the spinors | <p>[01:33:43] So we've, we've restricted ourselves to one gauge group, this big unitary group on the spinors using whatever sort of inner product naturally exists on the spinors. And not spinors valued in an auxiliary structure, but intrinsic spinors. | ||
<p>[01:34:00] The toolkit that we have is that the adjoint bundle looks like the Clifford algebra at the level of vector space. | <p>[01:34:00] The toolkit that we have is that the adjoint bundle, $$ad(P_U(128))$$ looks like the Clifford algebra $$Cl$$ at the level of vector space. | ||
<p>[01:34:28] Which is just looking like the exterior algebra on the | <p>[01:34:28] Which is just looking like the exterior algebra, $$\wedge^{*}(C)$$ on the chimeric bundle; that means that it is graded by degrees. [The] chimeric bundle has dimension-14, so there's a zero-part, a one-part, a two-part, all the way up to 14. Plus, we have forms in the manifold. And so the question is if I want to look at $$\Omega^i$$ valued in the adjoint bundle, there's going to be some element $$\Phi_{i}$$, which is pure trace. | ||
<p>[01:35:12] Right? Because it's the same representations appearing where in the usually auxiliary directions as well as the geometric directions. So we get an entire suite of invariance together with trivially associated invariants that come from using the Hodge star operator on the forms. I'm just going to call them for completeness. | <p>[01:35:12] Right? Because it's the same representations appearing where in the usually auxiliary directions as well as the geometric directions. So we get an entire suite of invariance together with trivially associated invariants that come from using the Hodge star operator on the forms. I'm just going to call them for completeness. | ||