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Theory of Geometric Unity: Difference between revisions
→Starting point: three observations by Edward Witten
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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 | |||
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| '''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 === | ||