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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 17:06, 15 March 2021
, 15 March 2021→The Current Picture of Physics
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$$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = 8 \pi T_{\mu\nu}$$ | <div style="text-align: center; margin-left: auto; margin-right: auto;">$$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = 8 \pi T_{\mu\nu}$$</div> | ||
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$$ \text{SU}(3) \text{ (color)} \times \text{SU}(2) \text{ (weak isospin)} \times \text{U}(1) \text{ (weak hypercharge)}$$ | <div style="text-align: center; margin-left: auto; margin-right: auto;">$$ \text{SU}(3) \text{ (color)} \times \text{SU}(2) \text{ (weak isospin)} \times \text{U}(1) \text{ (weak hypercharge)}$$</div> | ||
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$$d^*_A F_A = J(\psi)$$ | <div style="text-align: center; margin-left: auto; margin-right: auto;">$$d^*_A F_A = J(\psi)$$</div> | ||
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$$ \unicode{x2215}\kern-0.7em D_A \psi = m \psi $$ | <div style="text-align: center; margin-left: auto; margin-right: auto;">$$ \unicode{x2215}\kern-0.7em D_A \psi = m \psi $$</div> | ||
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$$ P_E(F_{\nabla^{LC} h}) \neq h^{-1}P_E(F_{\nabla^{LC}}) h $$ | <div style="text-align: center; margin-left: auto; margin-right: auto;">$$ P_E(F_{\nabla^{LC} h}) \neq h^{-1}P_E(F_{\nabla^{LC}}) h $$</div> | ||
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''[https://youtu.be/Z7rd04KzLcg?t=3461 00:57:41]''<br> | ''[https://youtu.be/Z7rd04KzLcg?t=3461 00:57:41]''<br> | ||
There are other possibilities that while each of these may be simplest in its category, they are not simplest in their interaction. For example, we know that Dirac famously took the square root of the Klein-Gordon equation to achieve the Dirac equation—he actually took two square roots, one of the differential operator, and another of the algebra on which it acts. But could we not do the same thing by re-interpreting what we saw in Donaldson theory and Chern-Simons theory, and finding that there are first-order equations that imply second-order equations that are nonlinear in the curvature? So let's imagine the following: we replace the standard model with a true second-order theory. We imagine that general relativity is replaced by a true first-order theory. And then we find that the true second-order theory admits of a square root and can be linked with the true first-order theory. This would be a program for some kind of unification of Dirac's type, but in the force sector. The question is, "Does this really make any sense? Are there any possibilities to do any such thing?" | There are other possibilities that while each of these may be simplest in its category, they are not simplest in their interaction. For example, we know that Dirac famously took the square root of the Klein-Gordon equation to achieve the Dirac equation—he actually took two square roots, one of the differential operator, and another of the algebra on which it acts. But could we not do the same thing by re-interpreting what we saw in Donaldson theory and Chern-Simons theory, and finding that there are first-order equations that imply second-order equations that are nonlinear in the curvature? So let's imagine the following: we replace the standard model with a true second-order theory. We imagine that general relativity is replaced by a true first-order theory. And then we find that the true second-order theory admits of a square root and can be linked with the true first-order theory. This would be a program for some kind of unification of Dirac's type, but in the force sector. The question is, "Does this really make any sense? Are there any possibilities to do any such thing?" | ||
=====Motivations for Geometric Unity===== | =====Motivations for Geometric Unity===== | ||