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 17:21, 25 April 2020
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<p>[01:22:36] At least in Euclidean signature. We can get to mixed signatures later. From that, we can form the associated bundle, $$\Gamma^{\infty}(P_{U(8)}) \times_{ad}\U($))$$. | <p>[01:22:36] At least in Euclidean signature. We can get to mixed signatures later. From that, we can form the associated bundle, $$\Gamma^{\infty}(P_{U(8)}) \times_{ad}\U($))$$. | ||
<p>[01:22:54] And sections of this bundle are either, depending upon how you want to think about it, the gauge group, $$H$$ or $$\Xi$$, a space of sigma fields. Nonlinear. | <p>[01:22:54] And sections of this bundle are either, depending upon how you want to think about it, the gauge group, $$H$$, or $$\Xi$$, a space of sigma fields. Nonlinear. | ||
<p>[01:23:25] There's no reason that we can't choose this as field content. Again, we're being led by the nose like a bull. If we want to make use of the symmetries of the theory, we have to promote some symmetry to being part of the theory, and we have to let it be subjected to dynamical laws. We're going to lose control over it. | <p>[01:23:25] There's no reason that we can't choose this as field content. Again, we're being led by the nose like a bull. If we want to make use of the symmetries of the theory, we have to promote some symmetry to being part of the theory, and we have to let it be subjected to dynamical laws. We're going to lose control over it. | ||