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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 17:31, 14 April 2020
, 14 April 2020→Part III: Starting in on Physics: Zeta -> zeta and Nu -> nu
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<p>[01:55:03] Well, there are different, depending upon whether you take the degree-zero piece together with the degree-two piece, or you take the degree-one piece, let's just take the degree-one piece. | <p>[01:55:03] Well, there are different, depending upon whether you take the degree-zero piece together with the degree-two piece, or you take the degree-one piece, let's just take the degree-one piece. | ||
<p>[01:55:16] You get some kind of equation. So I'm going to decide that I have a $$\ | <p>[01:55:16] You get some kind of equation. So I'm going to decide that I have a $$\zeta$$ field, which is an $$\Omega^{1}$$ tensor spinors and a field $$\nu$$, which always strikes me as a Yiddish field. $$\nu$$ is $$\Omega^{0}$$ tensor S. | ||
<p>[01:55:47] What equation would they solve if we were doing Hodge theory relative to this complex? The equation would look something like this. | <p>[01:55:47] What equation would they solve if we were doing Hodge theory relative to this complex? The equation would look something like this. | ||
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<p>[01:57:48] Now, if you have something like that, that would be a hell of a Dirac equation. Right. You've got differential operators over here. You've got differential operators. I guess I didn't write them in. But you would have two differential operators over here, and you'd have this differential operator coming from this [[Maurer-Cartan form]]. So I apologize, I'm being a little loose here, but the idea is you have two of these terms are zeroth-order. Three of these terms would be first order, and on this side, one term would be first-order. | <p>[01:57:48] Now, if you have something like that, that would be a hell of a Dirac equation. Right. You've got differential operators over here. You've got differential operators. I guess I didn't write them in. But you would have two differential operators over here, and you'd have this differential operator coming from this [[Maurer-Cartan form]]. So I apologize, I'm being a little loose here, but the idea is you have two of these terms are zeroth-order. Three of these terms would be first order, and on this side, one term would be first-order. | ||
<p>[01:58:27] And that's not there. That's fine. That was a mistake. Oh, no, sorry. That was a mistake, calling it a mistake. These are two separate equations, right? So you have two separate fields, $$\ | <p>[01:58:27] And that's not there. That's fine. That was a mistake. Oh, no, sorry. That was a mistake, calling it a mistake. These are two separate equations, right? So you have two separate fields, $$\nu$$ and $$\zeta$$, and you have a coupled set of differential equations that are playing the role of the Dirac theory. Coming from the Hodge theory of a complex, whose obstruction to being cohomology theory, would be the replacement to the Einstein field equations, which would be rendered gauge invariant on a group relative to a tilted subgroup. | ||
<p>[01:58:50] So now we've dealt with two of the three sectors. Is there any generalization of the Yang-Mills equation? Well, if we were to take the Einstein field equation generalization and take the norm square of it. Oh, there's some point I should make here. | <p>[01:58:50] So now we've dealt with two of the three sectors. Is there any generalization of the Yang-Mills equation? Well, if we were to take the Einstein field equation generalization and take the norm square of it. Oh, there's some point I should make here. | ||