2007/12/17 by Samuel L. Marateck, Marateck, Samuel L.
Engineering · Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Magnetic Field Sensors Techniques #Geomagnetism and Paleomagnetism Studies #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.0712.2623
The Yang-Mills field strength incorporating a non-Abelian feature is one of the cornerstones of the standard model. Although Yang-Mills gauge theories have been around for over fifty years, surprisingly the derivation of the Yang-Mills field strength using classical gauge theory does not appear anywhere in the literature. In their 1954 paper, Yang and Mills had to invent a non-Abelian field strength to satisfy certain criteria. In Section 5 we use Yang's gauge transformation in a heuristic derivation of the Yang-Mills field strength. The preceding sections cover material relating to the derivation. Section 3 shows where Pauli in the article cited by Yang and Mills gives an expression for the electro-magnetic field strength in terms of a commutator. For some reason, Yang and Mills did not use this approach.