Topology, Differential Geometry, and Lie Groups

The latest volume in the TRiPS series (Texts and Readings in the Physical Sciences) published by the Hindustan Book Agency is Lectures on Advanced Mathematical Methods for Physicists by Sunil Mukhi of the Tata Institute of Fundamental Research, Mumbai, and N. Mukunda of the IISc, Bangalore.

Mukhi and Mukunda are masters of the game, renowned expositors of a field that is often difficult to fathom for the lay mortal. But anyone- mortal or not- who would like to understand many aspects of modern physics, ranging from gravitation to particle and nuclear physics will find this book indispensable.

The book is in two parts. The first provides a simple introduction to basic topology, followed by a survey of homotopy. Calculus of differentiable manifolds is then developed, and a Riemannian metric is introduced along with the key concepts of connections and curvature. The final chapters lay out the basic notions of simplicial homology and De Rham cohomology as well as fibre bundles, particularly tangent and cotangent bundles.

Part II starts with a review of group theory, followed by the basics of representation theory. A thorough description of Lie groups and algebras is presented with their structure constants and linear representations. Root systems and their classifications are detailed, and this section of the book concludes with the description of representations of simple Lie algebras, emphasizing spinor representations of orthogonal and pseudo-orthogonal groups.

The style of presentation is succinct and precise. Involved mathematical proofs that are not of primary importance to physics student are omitted. The book aims to provide the reader access to a wide variety of sources in the current literature, in addition to being a textbook of advanced mathematical methods for physicists.

In our Physics and Mathematics sections, in hardcover, 286 pages. Rs 500. ISBN 9789380250021