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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.
Preface
Notation and Convention
1:Hamiltonian Systems and Applications
2:Schrödinger Equation and Quantum Mechanics
3:Maxwell Equations, Dirac Monopole, and Gauge Fields
4:Special Relativity
5:Abelian Gauge Field Equations
6:Dirac Equations
7:Ginzburg–Landau Equations for Superconductivity
8:Magnetic Vortices in Abelian Higgs Theory
9:Non-Abelian Gauge Field Equations
10:Einstein Equations and Related Topics
11:Charged Vortices and Chern–Simons Equations
12:Skyrme Model and Related Topics
13:Strings and Branes
14:Born–Infeld Theory of Electromagnetism
15:Canonical Quantization of Fields
Appendices
Bibliography
Index
Description
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.
