Graph, Wall, Tome: Difference between revisions
ââGraph: Added missing word in Graph transcription âAardvark
(ââGraph: This simplified version probably works better in mobile. Side-by-side seemed awkward to me. Let me know if I'm missing something.) |
(ââGraph: Added missing word in Graph transcription âAardvark) Tags: Mobile edit Mobile web edit  |
||
| Line 66: | Line 66: | ||
(ii) Over <math>M</math> is a vector bundle <math>X</math> with a non-abelian gauge group <math>G</math>. | (ii) Over <math>M</math> is a vector bundle <math>X</math> with a non-abelian gauge group <math>G</math>. | ||
(iii) Fermions are sections of <math>(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}})</math>. <math>R</math> and <math>\tilde{R}</math> are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in representation difference <math>\Delta</math> in some underlying theory. | (iii) Fermions are sections of <math>(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}})</math>. <math>R</math> and <math>\tilde{R}</math> are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in a representation difference <math>\Delta</math> in some underlying theory. | ||
All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms. | All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms. | ||