Traditional literature in mathematical physics is clustered around
classical mechanics, especially fluids and elasticity. This book
reflects the modern development of theoretical physics in the areas of
field theories: classical, quantum, and gravitational, in which
differential equations play essential roles and offer powerful insight.
Yang here 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. Much emphasis is given to the
mathematical and physical content offering an appreciation of the
interplay of mathematics and theoretical physics from the viewpoint of
differential equations. Advanced methods and techniques of modern
nonlinear functional analysis are kept to a minimum and each chapter is
supplemented with a collection of exercises of varied depths making it
an ideal resource for students and researchers alike.
