Difference between revisions of "Editing the Graph"

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.

This is a modified version of the paragraph:

<div style="font-weight:bold;line-height:1.6;">Edited Graph Version 1</div>

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

# [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].

# The masses of elementary particles are generated through the Higgs mechanism.

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.