By Gregory L. Naber
This quantity is meant to hold at the application, initiated in Topology, Geometry, and Gauge Fields: Foundations (Springer, 2010), of exploring the interrelations among particle physics and topology that come up from their shared idea of a gauge box. The textual content starts off with a synopsis of the geometrical history assumed of the reader (manifolds, Lie teams, bundles, connections, etc.). There follows a long, and a bit casual dialogue of many of the most simple of the classical gauge theories coming up in physics, together with classical electromagnetic conception and Dirac monopoles, the Klein-Gordon and Dirac equations and SU(2) Yang-Mills-Higgs conception. the genuine goal here's to witness things like spacetime manifolds, spinor buildings, de Rham cohomology, and Chern periods come up in their personal accord in significant physics. All of those are then constructed conscientiously within the last chapters. With definitely the right definitions in hand, you could, for instance, totally establish magnetic cost and instanton quantity with the Chern numbers of the bundles on which the cost and instanton reside, and discover the obstruction to the lifestyles of a spinor constitution within the kind of the second one Stiefel-Whitney type. This moment version of the booklet comprises, in an Appendix, a far multiplied cartoon of Seiberg-Witten gauge concept, together with a quick dialogue of its origins in physics and its implications for topology. to supply the reader with the chance to pause en direction and take part the thrill, there are 228 workouts, every one an essential component of the advance and every positioned at exactly the aspect at which it may be solved with optimum gain.
Reviews of first variation:
“Naber’s target isn't really to educate a sterile direction on geometry and topology, yet fairly to allow us to determine the topic in motion, via gauge theory.” (SIAM Review)
“The presentation … is enriched via specific discussions concerning the actual interpretations of connections, their curvatures and attribute periods. I rather loved bankruptcy 2 the place many basic actual examples are mentioned at nice size in a reader pleasant model. No element is left to the reader’s mind's eye or interpretation. i'm really not conscious of one other resource the place those extremely important examples and concepts are provided at a degree available to beginners.” (Mathematical Reviews)