The idea of a gauge theory evolved from the work of hermann weyl. China 4 school of mathematics, university of science and technology of china, wu wen tsun key laboratory of. Modern differential geometry in gauge theories yangmills fields. N 4 supersymmetric yangmills theory and its deformations. Quantum yangmills theory clay mathematics institute. The library of congress chronicling america the seattle postintelligencer. Yangmills theory is a gauge theory based on a special unitary group sun, or more generally. We consider classical yangmills theory with point sources and derive equations of motion for the coupled particlefield system. Part 2 is devoted to supersymmetry, superspace formalism and supersym metric yangmills theory. Yangmills theory and geometry imperial college london.
The purpose of this section is to introduce this theory and some of its properties. The basic idea behind the yangmills approach presented here, is seen in many books on group theory. One may now copy a standard textbook derivation 43 to show that. Both of these books discuss quantum field theory in condensed matter physics. An introduction to generalized yang mills theories m. All action is for the sake of some end, and rules of action, it seems natural to suppose, must take their whole character and colour from the end to which they are subservient. Su3 yang mills theory in any detail, but in principle it is easy to construct using the recipe i will explain. More generally, yang mills theories contain gauge elds and matter elds like. The answer is yes, and the resulting theory is known as yang mills. Yangmills is a strongly coupled quantum field theory, whose lowenergy dynamics looks nothing at all like. Yang mills theory and the abc conjecture yanghui he1. Yang mills theory pure electromagnetism is a free theory of a massless spin 1.
Yang mills theory had a profound effect on the development of differential and algebraic geometry over the last quarter of the twentieth century, and it is now clear that this should be seen as part of a larger phenomenon. The most important quantum field theories qfts for describing elementary particle physics are gauge theories. The simplest of these theories are the supersymmetric yangmills theories. On the geometry of yangmills and gravitational gauge theories. Mills theory is pure yang mills theory with action sa 1 2 z d4xtracef f.
Yangmills theory, so named the discoverers can exhibit complicated physics. G, and construct the corresponding yang mills theory. Geometrodynamics of gauge fields on the geometry of yangmills. Topics such as the dynamics of yangmills theories, instanton solutions and.