A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
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<p>[02:20:49] Who and what correspond to bosons and fermions. And how and why correspond to equations and the Lagrangian that generates them. So, if you think about those six quantities, you'll realize that that's really what the content of a fundamental theory is assuming that it can be quantized properly. Most fields and, in this case, we're going to call the collection of two-tuples $$\omega$$. So the inside of $$\omega$$ that will be in the first tuple will have $$\epsilon$$ and $$\varpi$$ written sort of an nontraditional variation of how we write this symbol for $$\varpi$$. In the second tuple, we'll have the letters, $$\nu$$ and $$\zeta$$. And I would like them not to move because they honor particular people who are important (NB: children are named N. and Z.). | <p>[02:20:49] Who and what correspond to bosons and fermions. And how and why correspond to equations and the Lagrangian that generates them. So, if you think about those six quantities, you'll realize that that's really what the content of a fundamental theory is assuming that it can be quantized properly. Most fields and, in this case, we're going to call the collection of two-tuples $$\omega$$. So the inside of $$\omega$$ that will be in the first tuple will have $$\epsilon$$ and $$\varpi$$ written sort of an nontraditional variation of how we write this symbol for $$\varpi$$. In the second tuple, we'll have the letters, $$\nu$$ and $$\zeta$$. And I would like them not to move because they honor particular people who are important (NB: children are named N. and Z.). | ||
<p>[02:21:36] So most fields, in this case, $$\ | <p>[02:21:36] So most fields, in this case, $$\omega$$, are dancing on $$Y$$, which was called $$U$$ in the lecture, unfortunately, but they are observed via pullback as if they lived on $$X$$. In other words, if you're sitting in the stands, you might feel that you're actually literally on the pitch, even though that's not true. So what we've done is we've taken the U of Wheeler, we've put it on its back and created a double-U ("W") structure. | ||
<p>[02:21:59] And the W structure is meant to say that there's a bundle on top of a bundle. Again, geometric unity is more flexible than this, but I wanted to make the most concrete approach to this possible for at least this introduction. We don't need to state that Y would, in fact, be a bundle A. It could be an immersion of $$X$$ into any old manifold. But I, I'd like to go with the most ambitious version of GU first. So the two projection maps are $$\pi_2$$ and $$\pi_1$$. And what we're going to say up top is that we're going to have a symbol $$Z$$ and an action of a group $$\rho$$ on $$Z$$, standing in for any bundle associated to the principle bundle, which is generated as the unitary bundle of the spin of the spinors on the chimeric tangent bundle to $$Y$$. | <p>[02:21:59] And the W structure is meant to say that there's a bundle on top of a bundle. Again, geometric unity is more flexible than this, but I wanted to make the most concrete approach to this possible for at least this introduction. We don't need to state that Y would, in fact, be a bundle A. It could be an immersion of $$X$$ into any old manifold. But I, I'd like to go with the most ambitious version of GU first. So the two projection maps are $$\pi_2$$ and $$\pi_1$$. And what we're going to say up top is that we're going to have a symbol $$Z$$ and an action of a group $$\rho$$ on $$Z$$, standing in for any bundle associated to the principle bundle, which is generated as the unitary bundle of the spin of the spinors on the chimeric tangent bundle to $$Y$$. | ||