Jump to content

A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

Line 572: Line 572:
<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 $$A_\{pi}$$.
<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 $$U$$.
Anonymous user