Editing the Graph: Difference between revisions

|project=Editing the Graph

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Though the original Graph aptly describes our physical knowledge, there are some minor alterations and additions to be made for it to accurately capture the present understanding.

The Graph is a paragraph from Edward Witten's paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry], at the bottom of page 20:

<div style="font-weight:bold;line-height:1.6;">The Original Graph</div>

If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations:

 

 

(iii) Fermions are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}})$$. $$R$$ and $$\tilde{R}$$ are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in representation difference $$\Delta$$ 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.

<div style="font-weight:bold;line-height:1.6;">Edited Graph Version 2</div>

If one wants to summarize our knowledge of physics in the briefest possible terms, there are four really fundamental observations:

 

2. Over `M` is a principal bundle 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.

4. Yukawa couplings between the fermion field and the Higgs field endow fermions with the property of mass. Massive bosons also acquire their mass through this Higgs mechanism.