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

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<p>[00:43:47] The second fundamental insight... I'm going to begin to start drawing pictures here as well.

<p>[00:43:55] So, if this is the space-time manifold, "the arena"; the second one concerns symmetry groups which cannot necessarily be deduced from any structure inside of "the arena". They are additional data that come to us out of the blue without explanation and these symmetries for a non-Abelian group, which is currently SU(3) "color" ~~cross~~ SU(2) "weak" ~~cross~~ U(1) "weak hypercharge", which breaks down to SU(3) ~~cross U~~(1), where the broken U(1) is the electromagnetic symmetry.

<p>[00:43:55] So, if this is the space-time manifold, "the arena"; the second one concerns symmetry groups which cannot necessarily be deduced from any structure inside of "the arena". They are additional data that come to us out of the blue without explanation and these symmetries for a non-Abelian group, which is currently SU(3) "color" x SU(2) "weak" x U(1) "weak hypercharge", which breaks down to SU(3)xU(1), where the broken U(1) is the electromagnetic symmetry.

<p>[00:44:54] This equation is also a curvature equation, the corresponding equation, the curvature of an auxiliary structure known as a gauge potential when differentiated in a particular way is equal, again, to the amount of stuff in the system that is not directly involved in the left-hand side of the equation. So, it has many similarities to the above equation. Both involve curvature. One involves a projection or a series of projections. The other involves a differential operator.