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Theory of Geometric Unity: Difference between revisions
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== Background == | == Background == | ||
[[File:GU_triangle.png| | [[File:GU_triangle.png|500px|right]] | ||
[[File:Geometric unity puzzle pieces.png|500px|right]] | |||
Cornerstones of modern physics | |||
{| class="wikitable" | {| class="wikitable" | ||
| '''1.''' The Arena (<math> Xg_{\mu\nu}</math>) | | '''1.''' The Arena (<math> Xg_{\mu\nu}</math>) | ||
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| <math>\partial_A \psi = m \psi</math> | | <math>\partial_A \psi = m \psi</math> | ||
|} | |} | ||
'''Key guiding question:''' what are the compatibilities and incompatibilities on the geometric level before the theory is created quantum mechanical. | |||
* From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection of the metric $P_E(F_A)$ | |||
* From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection $d^\star_A F_A$ | |||
'''Question:''' What if the $F_A$'s are the same in both contexts? | |||
Then we're applying two different operators. The Einstein projection operator is zeroth order, it's destructive in the sense that it doesn't see the entire curvature tensor. The adjoint exterior derivative operator is inclusive but of first order. | |||
'''Question:''' Is there any opportunity to combine these two operators? | |||
== Layman Explanation == | |||
a theory is like a newspaper story | a theory is like a newspaper story | ||