Yang-Mills Fields: Semi Classical Aspects

Abstract

Gauge theories have been formulated in 1954 by Yang and Mills [1] as natural non abelian generalizations of Maxwell’s theory of the electromagnetic field. Since the electromagnetic field mediates electromagnetic interactions between charged svstems it was natural to seek for the non abelian analog susceptible to accomodate the non abelian internal symmetries discovered in the realm of elementary particle physics. The naturalness of this construction seems also to have drawn the attention of other physicists who were simultaneously aware of a number of difficulties which remain unsolved even now. As time went, more approximate internal symmetries [2] were discovered in particle physics. Also, a number of fundamental remarks of a technical nature [3] allowed to put gauge theories to practical use. There resulted a net progress in unifying “weak”, “electromagnetic”, [4][5], and “strong” interactions [5] between elementary particles, to such an extent that at present, it has become standard to think about particle physics in terms of gauge theories [6]. The naturalness of these theories has also appeared in mathematics where it constitutes a branch of differential geometry: the study of fiber bundles and connections on them [7], associated with a Lie group G-[4][5][8].