Gauge symmetries and fibre bundles : applications to particle dynamics / A. P. Balachandran ... [et al.]

This short book, written by physicists, contains an introduction to the concepts of differential geometry used in modern descriptions of gauge theories and spinning particles. The scope of the book and the style adopted by the authors can be inferred from the following excerpts from the introduction: "A theory defined by an action which is invariant under a time-dependent group of transformations can be called a gauge theory. The underlying mathematical structures of gauge theories have been studied for a long time in mathematics under the name of fibre bundles. Simple systems with gauge invariance occur in plentiful quantities in the mechanics of point particles and extended objects. We introduce in Chapters 3 and 4 the notion of fibre bundles in the context of a discussion on spinning point particles and Dirac monopoles. The classical description of Yang-Mills particles with internal degrees of freedom, such as isospin or colour, is given in Chapter 6. In Chapter 7 we elaborate on a Kaluza-Klein description. The canonical formalism and quantization are discussed in Chapter 8. The procedure for obtaining an extension to supergroup manifolds is briefly discussed in Chapter 9.'' (MathScinet)