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A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
Revision as of 21:55, 15 March 2021
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What is physics to physicists today? How do they see it different from the way in which we might imagine the lay person sees physics? Ed Witten was asked this question in a talk he gave on physics and geometry many years ago, and he pointed us to three fundamental insights, which were his big three insights in physics. And they correspond to the three great equations. | What is physics to physicists today? How do they see it different from the way in which we might imagine the lay person sees physics? Ed Witten was asked this question in a talk he gave on physics and geometry many years ago, and he pointed us to three fundamental insights, which were his big three insights in physics. And they correspond to the three great equations. | ||
<blockquote style="background: #f3f3ff; border-color: #ddd;">If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Space-time is a pseudo-Riemannian manifold \(M\), endowed with a metric tensor and governed by geometrical laws. (ii) Over \(M\) is a vector bundle \(X\) with a nonabelian gauge group \(G\). (iii) Fermions are sections of \((\hat{S}{+} \otimes | <blockquote style="background: #f3f3ff; border-color: #ddd;">If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Space-time is a pseudo-Riemannian manifold \(M\), endowed with a metric tensor and governed by geometrical laws. (ii) Over \(M\) is a vector bundle \(X\) with a nonabelian gauge group \(G\). (iii) Fermions are sections of \((\hat{S}{+} \otimes V_{R}) \oplus (\hat{S}{-} \otimes V_{\tilde{R}})\). \(R\) and \(\tilde{R}\) not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in a 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 interpreted in quantum mechanical terms.<br> | ||
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Edward Witten, ''[https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry]''</blockquote> | Edward Witten, ''[https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry]''</blockquote> | ||