Mathematical Physics:With Applications, Problems & Solutions

Abstract

This is a very unusual book, 852 pages long with 32 chapters. The author, V. Balakrishnan is an eminent theoretical physicist who has inspired a generation of students at IIT Madras over more than three decades. Bala, as popularly known amongst friends, is well known for his breadth of knowledge in various areas of theoretical physics. There are very few theoretical physicists who have written important papers in widely different areas like high energy physics, condensed matter physics, equilibrium and non-equilibrium statistical mechanics and nonlinear dynamics as Bala has done. So when I heard of a book on mathematical physics by Bala, I was curious about its contents. After carefully going through it, I can only compare it with some of the classics of mathematical physics like Methods of Theoretical Physics , vols I and II by Morse and Feshback, and Methods of Mathematical Physics , vols I and II by Courant and Hilbert. And I am happy to note that it is of similar level, but very different from the other two books. It is not only different in its content (which is to be expected since many new topics have become important in the last 50 years or so), but more important in its emphasis. In particular, this book assigns a prominent role to the applications of the relevant mathematics to different areas of physics ranging from fluid dynamics, electromagnetic theory, quantum mechanics, special theory of relativity, quantum optics, random processes, linear response theory, and so on. The emphasis in the book is not on formal proofs but rather on motivating and elaborating the results and even more important, discussing the relevance of the results in different areas of physics. Bala knows very well that one can never learn mathematical physics (actually even theoretical physics) without solving problems. With this in mind, he has given about 370 problems, many of them with several parts and sub-parts. He has made the problems contiguous with the text and has provided solutions to them either in the outline or in detail at the end of each chapter. This I consider as an important aspect of the book. I believe that over the years this book will occupy a place similar to the other classics in the field, like the two books mentioned above.