3 ms·

Note the article is by Nobel Laureate C.N. Yang [1] who also worked with James Simons and co-authored what has become known as the "Wu-Yang Dictionary" [2]. [1

by espeed 9y ago

Note the article is by Nobel Laureate C.N. Yang [1] who also worked with James Simons and co-authored what has become known as the "Wu-Yang Dictionary" [2]. [1] Yang-Mills Theory: https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory [2] "Wu-Yang Dictionary" http://www.indiana.edu/~jpac/QCDRef/1970s/Concept%20of%20nonintegrable%20phase%20factor%20and%20global%20formulation%20of%20gauge%20fields%20-%20Wu,%20Yang%20-%201975.pdf http://www.indiana.edu/~jpac/QCDRef/1970s/Concept%20of%20non... ...The mathematics of these results is in fact well known to the mathematicians in fiber bundle theory. An identification table of terminologies is given in Sec. V. We should emphasize that our interest in this paper does not lie in the beautiful, deep, and general mathematical development in fiber bundle theory. Rather we are concerned with the necessary concepts to describe the physics of gauge theories. It is remarkable that these concepts have already been intensively studied as mathematical constructs. "Gauge Theory and Inflation: Enlarging the Wu-Yang Dictionary to a unifying Rosetta Stone for Geometry in Application" https://www.youtube.com/watch?v=h5gnATQMtPg https://www.youtube.com/watch?v=h5gnATQMtPg

zaph0d_ 9y ago
Thank you for the interessting material! I have heard a lecture on the geometric and topological applications to solid-state physics. This is one of the things that excites me a lot that whole areas of physics can be "geometrized".
- emmelaich 9y ago
  You've reminded me of Plato's quotes: "God ever geometrizes." and "Geometry existed before the creation."
- Retra 9y ago
  Part of me believes that geometry is really just a subset of human thinking that comes very naturally/quickly to us, and thus we are more successful studying physics through geometry than through less 'algebraic' frameworks. So we made the most advances there just because we are biased toward doing so. But then I think that we may be so strongly biased toward doing so because there's something fundamentally easy about evolving a brain that comprehends geometry. That information with geometric representations are fundamentally easier to evolve good mental models for than other kinds of information.

by espeed 9y ago

zaph0d_ 9y ago

Thank you for the interessting material! I have heard a lecture on the geometric and topological applications to solid-state physics. This is one of the things that excites me a lot that whole areas of physics can be "geometrized".

emmelaich 9y ago
You've reminded me of Plato's quotes: "God ever geometrizes." and "Geometry existed before the creation."
Retra 9y ago
Part of me believes that geometry is really just a subset of human thinking that comes very naturally/quickly to us, and thus we are more successful studying physics through geometry than through less 'algebraic' frameworks. So we made the most advances there just because we are biased toward doing so. But then I think that we may be so strongly biased toward doing so because there's something fundamentally easy about evolving a brain that comprehends geometry. That information with geometric representations are fundamentally easier to evolve good mental models for than other kinds of information.