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

[[File:GU Presentation Powerpoint Summary Diagram Slide.png|thumb|right]]

[[File:GU Presentation Powerpoint Summary Diagram Slide.png|thumb|right]]

So our summary diagram looks something like this. Take a look at the \(\tau_{A_0}\). We will find a homomorphism of the gauge group into its inhomogeneous extension that isn't simply inclusion under the first factor. We—and I'm realizing that I have the wrong pi projection, that should just be a simple \(\pi\) projecting down. We have a map from the inhomogeneous gauge group via the bi-connection to \(A \times A\), connections cross connections, and that behaves well according to the difference operator \(\delta\) that takes the difference of two connections and gives an honest ad-valued one-form.

So our summary diagram looks something like this. Take a look at the \(\tau_{A_0}\). We will find a homomorphism of the gauge group into its inhomogeneous extension that isn't simply inclusion under the first factor. We—and I'm realizing that I have the wrong pi projection, that should just be a simple \(\pi\) projecting down. We have a map from the inhomogeneous gauge group via the bi-connection to \(A \times A\), connections cross connections, and that behaves well according to the difference operator \(\delta\) that takes the difference of two connections and gives an honest ad-valued one-form.

''[https://youtu.be/Z7rd04KzLcg?t=8963 02:29:23]''<br>

''[https://youtu.be/Z7rd04KzLcg?t=8963 02:29:23]''<br>

The infinitesimal action of a gauge transformation, or at least an infinitesimal one, on a point inside of the group is given by a somewhat, almost familiar expression, which should remind us of how the first term in the gauge deformation complex for self-dual Yang-Mills actually gets started. And so, by acting via this interesting embedding of the gauge group inside its inhomogeneous extension, but the non-trivial one, we get something very close to the original first step of the two-step deformation complex.

The infinitesimal action of a gauge transformation, or at least an infinitesimal one, on a point inside of the group is given by a somewhat, almost familiar expression, which should remind us of how the first term in the gauge deformation complex for self-dual Yang-Mills actually gets started. And so, by acting via this interesting embedding of the gauge group inside its inhomogeneous extension, but the non-trivial one, we get something very close to the original first step of the two-step deformation complex.

==== Sector III: Toolkit for the Unified Field Content ====

==== Sector III: Toolkit for the Unified Field Content ====