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 22:39, 15 April 2020
, 15 April 2020→Part II: Unified Field Content
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<p>[01:31:15] So right now, our field content is looking pretty good. It's looking unified in the sense. That it has an algebraic structure that is not usually enjoyed by field content and the field content from different sectors can interact and know about each other. Mmm. Provided we can drag something of this out of this with meaning. | <p>[01:31:15] So right now, our field content is looking pretty good. It's looking unified in the sense. That it has an algebraic structure that is not usually enjoyed by field content and the field content from different sectors can interact and know about each other. Mmm. Provided we can drag something of this out of this with meaning. | ||
<p>[01:31:38] Now, what would it mean to be able to use a gauge group in an intrinsic theory like this? We would be talking. About something like an action, let's say a first-order action and it would take the group $$\mathcal{G}$$, let's say to the $$\mathbb{R}$$. Invariant, not under the full group, but under the tilted gauge subgroup. And now the question is, do we have any such actions that are particularly nice? And could we recognize them the way Einstein did by trying to write down, not the action and Hilbert was the first one to write that down. But I, you know, I always feel defensive, uh, because I think Einstein and Grossmann did so much more to begin the theory in that the Lagrangian that got written down was really just an inevitability. | <p>[01:31:38] Now, what would it mean to be able to use a gauge group in an intrinsic theory like this? We would be talking. About something like an action, let's say a first-order action and it would take the group $$\mathcal{G}$$, let's say to the $$\mathbb{R}$$. Invariant, not under the full group, but under the tilted gauge subgroup, $$\mathcal{H_{\tau}}$$. And now the question is, do we have any such actions that are particularly nice? And could we recognize them the way Einstein did by trying to write down, not the action and Hilbert was the first one to write that down. But I, you know, I always feel defensive, uh, because I think Einstein and Grossmann did so much more to begin the theory in that the Lagrangian that got written down was really just an inevitability. | ||
<p>[01:32:38] So just humor me for this talk, and let me call it the Einstein-Grossmann Lagrangian. Hilbert's certainly done fantastic things and has a lot of credit elsewhere, and he did do it first. But here what we had was that Einstein thought in terms of the differential of the action, not the action itself. So what we're looking for is equations of motion or some field, $$\alpha$$ where $$\alpha$$ belongs to the one-forms on the group. | <p>[01:32:38] So just humor me for this talk, and let me call it the Einstein-Grossmann Lagrangian. Hilbert's certainly done fantastic things and has a lot of credit elsewhere, and he did do it first. But here what we had was that Einstein thought in terms of the differential of the action, not the action itself. So what we're looking for is equations of motion or some field, $$\alpha$$ where $$\alpha$$ belongs to the one-forms on the group. | ||