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1. Space-time is a pseudo-Riemannian manifold `M`, endowed with a metric tensor and governed be geometrical laws | 1. Space-time is a pseudo-Riemannian manifold `M`, endowed with a metric tensor and governed be geometrical laws | ||
2. Over `M` is a principal bundle with a nonabelian structure group `G`. | 2. Over `M` is a principal bundle `P_{G}` with a nonabelian structure group `G`. | ||
3. Fermions are sections of `(\hat{S}_+ \otimes V_R) \oplus (\hat{S}_- \otimes V_{\tilde{R}})`. `R` and `\tilde{R}` are complex linear representations of `G` and thus are not isomorphic. Their failure to be isomorphic explains why the light fermions are light. | 3. Fermions are sections of `(\hat{S}_+ \otimes V_R) \oplus (\hat{S}_- \otimes V_{\tilde{R}})`. `R` and `\tilde{R}` are complex linear representations of `G` and thus are not isomorphic. Their failure to be isomorphic explains why the light fermions are light. | ||