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Difference between revisions of "A Portal Special Presentation- Geometric Unity: A First Look"
A Portal Special Presentation- Geometric Unity: A First Look (view source)
Revision as of 17:23, 17 March 2021
, 17:23, 17 March 2021→Somatic Complex and Two More Operators
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''[https://youtu.be/Z7rd04KzLcg?t=6539 01:48:59]''<br> | ''[https://youtu.be/Z7rd04KzLcg?t=6539 01:48:59]''<br> | ||
Well, we know that \(\unicode{x2215}\kern-0.5em d_A\) composed with itself is going to be the curvature, and we know that we want that to be hit by a shiab operator. And if 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? And, then you realize that the information in the inhomogeneous gauge group, you actually have information not for one connection, but for two connections. | Well, we know that \(\unicode{x2215}\kern-0.5em d_A\) composed with itself is going to be the curvature, and we know that we want that to be hit by a shiab operator. And if 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? And, then you realize that the information in the inhomogeneous gauge group, you actually have information not for one connection, but for two connections. | ||
''[https://youtu.be/Z7rd04KzLcg?t=6584 01:49:44]''<br> | ''[https://youtu.be/Z7rd04KzLcg?t=6584 01:49:44]''<br> | ||
So in one case, I can do plus star to pick up the \(A_{\pi}\). But I am also going to have a derivative operator if I just do a star operation, so I need another derivative operator to kill it off here. So I'm going to take minus the derivative with respect to the connection, which defines a connection one-form as well as having the same derivative coming from the Levi-Civita connection on \(U\). | So in one case, I can do plus star to pick up the \(A_{\pi}\). But I am also going to have a derivative operator if I just do a star operation, so I need another derivative operator to kill it off here. So I'm going to take minus the derivative with respect to the connection, which defines a connection one-form as well as having the same derivative coming from the Levi-Civita connection on \(U\). | ||
[[File:OmegaDiagramMorePartlyLabelled.jpg|center]] | |||
''[https://youtu.be/Z7rd04KzLcg?t=6615 01:50:15]''<br> | ''[https://youtu.be/Z7rd04KzLcg?t=6615 01:50:15]''<br> | ||