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

So for example, if \(X\) was four-dimensional, therefore d equals 4, then \(Y\) in this case would be \(d^2\), which would be 16 plus 3d, which would be 12, making 28, divided by two, which would be 14. So in other words, a four-dimensional proto-spacetime—not a spacetime, but a proto-spacetime with no metric—would give rise to a 14-dimensional observerse portion called \(Y\). Now I believe that in the lecture in Oxford I called that \(U\), so I'm sorry for the confusion, but of course, this shifts around every time I take it out of the garage, and that's one of the problems with working on a theory in solitude for many years.

Most fields—and in this case we're going to call the collection of two-tuples \(\omega\), so inside of \(\omega\) that will be, in the first tuple we'll have \(ϵ\) and \(ϖ\), written in sort of a nontraditional variation of how we write this symbol for \(\pi\); 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. 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 structure.

We then get to shiab operators. Now, a '''shiab operator''' is a map from the group crossed the ad-valued \(i\)-forms. In this case, the particular shiab operator we're interested in is mapping \(i\)-forms to \((d - 3 + i)\)-forms. So for example, you would map a 2-form to \((d - 3 + i)\). So if \(d\), for example, were 14, and i were equal to two, then 14 minus three is equal to 11 plus two is equal to 13. So that would be an ad-valued \((14 - 1)\)-form, which is exactly the right place for something to form a current, that is, the differential of a Lagrangian on the space.