Mathematical Physics with Differential Equations

Abstract

Abstract This book presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general relativity, superconductivity, vortices and other topological solitons, and canonical quantization of fields, for which, knowledge and use of linear and nonlinear differential equations are essential for comprehension. With insight of differential equations, the book features itself in several aspects. Firstly, the presentation of the content follows a mathematically thorough and transparent style which serves to provide a handy and direct access to approach each of the subjects discussed. Secondly, it renders a fairly wide selection of themes which may further be tailored to suit individual preferences of a reader. Thirdly, it supplies a balanced pool of topics for seminars. Fourthly, it offers guidance and stimulation to the related contemporary research frontiers and literature. Much emphasis is given to the mathematical and physical content, implication, structures, and challenges of the governing differential equations of the theories encountered and developed, thus offering an appreciation of the interplay of mathematics and theoretical physics from the viewpoint of differential equations. On the other hand, advanced methods and techniques of modern nonlinear functional analysis are kept minimal. The book is comprised of fifteen topic chapters and an appendices chapter. Each chapter is supplemented with a collection of exercises of varied depths.