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This textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.
List of contents
- 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
About the author
Yisong Yang is a Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University. He received his Ph.D. in Mathematics from the University of Massachusetts at Amherst in 1988.
Summary
This textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.
