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

Abstract

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.