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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 00:40, 11 April 2020
, 11 April 2020→Part II: Unified Field Content
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<p>[01:36:27] And I can start to define operators. | <p>[01:36:27] And I can start to define operators. | ||
<p>[01:36:44] I'm used. So in this case, if I have a phi, which is one of these invariants in the form piece, I can either take a contraction or I can take a wedge product. In the Lie algebra piece, I can either take a Lie product. Or because I'm looking at, um, the unitary group, there's a second possibility, which is I can multiply everything by i and go from [[Skew-Hermitian]] to [[Hermitian] and take a [[Jordan product]] using anti commutators rather than commutators. | <p>[01:36:44] I'm used. So in this case, if I have a phi, which is one of these invariants in the form piece, I can either take a contraction or I can take a wedge product. In the Lie algebra piece, I can either take a Lie product. Or because I'm looking at, um, the unitary group, there's a second possibility, which is I can multiply everything by i and go from [[Skew-Hermitian]] to [[Hermitian]] and take a [[Jordan product]] using anti commutators rather than commutators. | ||
<p>[01:37:15] So I actually have a fair amount of freedom and I'm going to use a magic bracket notation, which in whatever situation I'm looking for, knows what it wants to be is does it want to do contraction? Does want to do wedge product, Lie product, Jordan product? But the point is, I now have a suite of ways of moving forms around. | <p>[01:37:15] So I actually have a fair amount of freedom and I'm going to use a magic bracket notation, which in whatever situation I'm looking for, knows what it wants to be is does it want to do contraction? Does want to do wedge product, Lie product, Jordan product? But the point is, I now have a suite of ways of moving forms around. | ||