Samuel Marateck | Searcharxiv

arXiv2012

Yang-Mills and Beyond

In their 1954 paper, Yang and Mills invented the non-Abelian field strength to satisfy certain criteria but didn't explain how it could be derived. In the penultimate section we show how the Yang-Mills field strength derives from Yang's gauge transformation. The preceding sections place Yang-Mills theory in historical perspective and cover material relating to the field strength. The final section shows how Yang-Mills theory was combined with spontaneous symmetry breaking, the Goldstone theorem and subsequent work to contribute to the Standard Model of particle physics.

physics.hist-ph↗

arXiv2009

The Differential Geometry and Physical Basis for the Applications of Feynman Diagrams

This paper recalls the development of gauge theory culminating in Yang-Mills theory, and the application of differential geometry including connections on fiber bundles to field theory. Finally, we see how the preceding is used to explain the Feynman diagrams appearing on the Feynman postage stamp released in May 2005. Version 2 included the Feynman diagrams, Version 3 corrected typos and Version 4 included an appendix for the derivation of the Yang-Mills transformation and field strength. Version 5 indicates that the article has been published in the Notices of the AMS and in July 2009 appears in Chinese translation in a journal of the Chinese Academy of Sciences. It also corrects some typos and adds to the appendix a heuristic derivation of the Yang-Mills field strength.

physics.hist-ph↗