|Geometry, Topology and Physics||Geometry and topology have become integral in the theoretical physicists tool kit. Ideas from geometry and topology are now fundamental in condensed matter physics, gravitational physics and particle theory.
Nakahara’s book Geometry, Topology and Physics provides an assessable introduction to these ideas.
The book is a massive expansion and revision of lectures given by Nakahara at the School of Mathematical and Physical Sciences, the University of Sussex back in 1986.
Chapters 1 and 2 provide a basic review of the physical and mathematical ideas need as a preliminary to the rest of the book. Most of this is familiar territory to a beginning graduate student in mathematical or theoretical physics.
Chapters 3 to 8 introduce some fundamental ideas in geometry and topology: homology groups, homotopy groups, manifolds, de Rham cohomology, Riemannian geometry and complex manifolds. Examples of the applications of these constructions in physics are given throughout these chapters.
Chapters 9 to 12 cover the topics of fibre bundles, connections & curvature, characteristic classes and the Atiyah-Singer index theorem. All these topics are fundamental in understanding gauge theories that form the backbone of the standard model.
The final chapters 13 and 14 describe anomalies in gauge theories and the bosonic string respectively. In a sense, these chapters bring all the ideas laid out earlier in the book together to describe some quite advanced mathematical physics.
Paperback: 596 pages
Publisher: Taylor & Francis; 2 edition (4 Jun 2003)