Difference between revisions of "Theory of Geometric Unity"

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| '''1.''' The Arena (<math> Xg_{\mu\nu}</math>)
| '''1.''' The Arena (<math> Xg_{\mu\nu}</math>)
| <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} =  \left( \frac{1}{c^4} 8\pi GT_{\mu\nu}\right)</math>
| <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} =  \left( \frac{1}{c^4} 8\pi GT_{\mu\nu}\right)</math>
| the Einstein equation, which governs gravity in the theory of general relativity


|-
|-
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<math> SU(3) \times SU(2) \times U(1)</math>
<math> SU(3) \times SU(2) \times U(1)</math>
| <math>d_A^*F_A=J(\psi)</math>
| <math>d_A^*F_A=J(\psi)</math>
| the Yang-Mills equation, which governs all other force fields in Yang-Mill-Maxwell theory
|-
|-
| '''3.''' Matter
| '''3.''' Matter
Antisymmetric, therefore light
Antisymmetric, therefore light
| <math>\partial_A \psi = m \psi</math>
| <math>\partial_A \psi = m \psi</math>
| the Dirac equation, which governs all matter particles
|}
|}


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* From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection of the metric $$P_E(F_{\Delta^LC})$$
* From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection of the metric $$P_E(F_{\Delta^LC})$$
* From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection $$d^\star_A F_A$$
* From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection $$d^\star_A F_A$$


=== Problem Nr. 1: Einstein's Theory of General Relativity is not a proper Gauge Theory ===
=== Problem Nr. 1: Einstein's Theory of General Relativity is not a proper Gauge Theory ===
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