User:ConceptHut: Difference between revisions

User:ConceptHut (edit)

2 bytes added , 5 February 2020

no edit summary

49

edits

@@ Line 17: / Line 17: @@
 # [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] : $$M$$, endowed with a [[metric tensor]] and governed by [https://en.wikipedia.org/wiki/Geometry geometrical laws].
 # Over $$M$$ is a [https://en.wikipedia.org/wiki/Vector_bundle vector bundle] : $$X$$, with a [https://en.wikipedia.org/wiki/Non-abelian_group non-abelian] [https://en.wikipedia.org/wiki/Gauge_theory gauge group] : $$G$$.
-# [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\bar{R}})$$. $$R$$ and $$\tilde{R}$$ are not [https://en.wikipedia.org/wiki/Isomorphism isomorphic]; their failure to be isomorphic explains why the light fermions are light.
+# [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\tilde{R}})$$. $$R$$ and $$\tilde{R}$$ are not [https://en.wikipedia.org/wiki/Isomorphism isomorphic]; their failure to be isomorphic explains why the light fermions are light.
 All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the [https://en.wikipedia.org/wiki/Introduction_to_gauge_theory gauge fields], and the fermions are to be interpreted in [https://en.wikipedia.org/wiki/Quantum_mechanics quantum mechanical] terms.