5,849
edits
Line 61: | Line 61: | ||
1. Space-time is a pseudo-Riemannian manifold `M`, endowed with a metric tensor and governed by geometrical laws | 1. Space-time is a pseudo-Riemannian manifold `M`, endowed with a metric tensor and governed by geometrical laws | ||
2. Over `M` is a principal bundle `P_{G}` with a nonabelian structure group `G`. | 2. Over `M` is a principal G-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. |