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 18:54, 25 April 2020
, 25 April 2020→GU III: Physics
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<p>[01:49:32] And, then you realize that the information in the inhomogeneous gauge group, you actually have information not for one connection, but for two connections. | <p>[01:49:32] And, then you realize that the information in the inhomogeneous gauge group, you actually have information not for one connection, but for two connections. | ||
<p>[01:49:44] In one case, I can do +* to pick up the $$A_\ | <p>[01:49:44] In one case, I can do +* to pick up the $$A_{\pi}$$. | ||
<p>[01:49:59] But I am also going to have a derivative operator if I just do a star operation. So, I need another derivative operator to kill it off here. So I'm going to take minus the derivative with respect to the connection, $$H^{-1}$$ $$d_{A_0}$$ $$H$$ which defines a connection one-form as well as having the same derivative coming from the Levi-Civita connection on $$U$$. | <p>[01:49:59] But I am also going to have a derivative operator if I just do a star operation. So, I need another derivative operator to kill it off here. So I'm going to take minus the derivative with respect to the connection, $$H^{-1}$$ $$d_{A_0}$$ $$H$$ which defines a connection one-form as well as having the same derivative coming from the Levi-Civita connection on $$U$$. | ||