ConceptHut
Joined 5 February 2020
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
TEST | |||
--- | --- | ||
== The Graph == | == The Graph == | ||
[[file:The-graph.png|600px]] | [[file:The-graph.png|600px]] | ||
Eric Weinstein suggested several alterations, that have been included above: | |||
* In (ii), “vector bundle X” should be changed to principal G-bundle. | |||
* Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G. | |||
* In (ii), “vector bundle X” should be changed to | |||
* Also in (ii), “nonabelian gauge group G” should be changed to | |||
* In (iii), <math>\ R</math> and <math>\tilde R</math> should be (complex) linear representations of G and so they are not equivalent. | * In (iii), <math>\ R</math> and <math>\tilde R</math> should be (complex) linear representations of G and so they are not equivalent. | ||
* He mentioned that some info was not required, and that higgs is remarkably absent. | * He mentioned that some info was not required, and that higgs is remarkably absent. | ||
This is a modified version of the paragraph by Edward Witten as [https://twitter.com/EricRWeinstein/status/928296366853328896?s=20 posted by Eric via Twitter]. | |||
<blockquote> | <blockquote> | ||
If one wants to summarise our knowledge of physics in the briefest possible terms, there are three really fundamental observations: | 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] : | # [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 | # Over $$M$$ is a [https://en.wikipedia.org/wiki/Principal_bundle principal bundle] : $$P_{G}$$, with a [https://en.wikipedia.org/wiki/Non-abelian_group non-abelian structure group] : $$G$$. | ||
# [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of | # [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\bar{R}})$$. $$R$$ and $$\bar{R}$$ are not [https://en.wikipedia.org/wiki/Isomorphism isomorphic]; their failure to be isomorphic explains why the light fermions are light. | ||
# Add something about Higgs | # Add something about Higgs | ||
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. | 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. | ||
</blockquote> | </blockquote> |