Mathematical Physics – Sadri Hassani – 2nd Edition

The goal of this book is to expose the reader to the indispensable role that mathematics—often very abstract—plays in modern . Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier , analysis, differential and integral equations, operator theory, and multi-dimensional Green’s functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories.

This second is a substantial revision of the first one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first , namely the balance between rigor and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the “unreasonable effectiveness of mathematics” in modern physics.

Einstein has famously said, “The most incomprehensible thing about nature is that it is comprehensible.” What he had in mind was reiterated in another one of his famous quotes concerning the question of how ” … mathematics, being after all a product of human thought, is so admirably appropriate to the objects of reality.” It is a question that comes to everyone’s mind when encountering the highly abstract mathematics required for a deep understanding of modern physics. It is the experience that Eugene Wigner so profoundly described as “the unreasonable effectiveness of mathematics in the natural sciences.”

  1. Preliminaries
  2. Vectors and Linear Maps
  3. Algebras
  4. Operator
  5. Matrices
  6. Spectral Decomposition
  7. Hilbert Spaces
  8. Classical Orthogonal Polynomials
  9. Fourier Analysis
  10. Complex Calculus
  11. Calculus of Residues
  12. Topics
  13. Separation of Variables in Spherical Coordinates
  14. Second-Order Linear Differential Equations
  15. Complex Analysis of SOLDEs
  16. Integral Transforms and Differential Equations
  17. Introductory Operator Theory
  18. Integral Equations
  19. Sturm-Liouville
  20. Green’s Functions in One Dimension
  21. Multidimensional Green’s Functions: Formalism
  22. Multidimensional Green’s Functions: Applications
  23. Group Theory
  24. Representation of Groups
  25. Representations of the Symmetric Group
Title: Mathematical Physics
Author: Sadri Hassani
Edition: 2nd Edition
ISBN: 978-3-319-01195-0
Type: eBook
Language: English
Mathematical Physics

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