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 18:18, 25 April 2020
, 25 April 2020→Unified Field Content Plus a Toolkit
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<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>[01:33:43] 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, $$ad( | <p>[01:34:00] The toolkit that we have is that the adjoint bundle, $$ad(P_{U(128)})$$ looks like the Clifford algebra, $$Cl$$, at the level of vector space. | ||
<p>[01:34:28] Which is just looking like the exterior algebra, $$\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}$$, which is pure trace. | <p>[01:34:28] Which is just looking like the exterior algebra, $$\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. | ||