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Mathematical Physics

A Modern Introduction to Its Foundations

  • Sadri Hassani

Table of contents

  1. Front Matter
    Pages I-XXXI
  2. Sadri Hassani
    Pages 1-16
  3. Finite-Dimensional Vector Spaces

    1. Front Matter
      Pages 17-17
    2. Sadri Hassani
      Pages 19-61
    3. Sadri Hassani
      Pages 63-100
    4. Sadri Hassani
      Pages 101-136
    5. Sadri Hassani
      Pages 137-168
    6. Sadri Hassani
      Pages 169-211
  4. Infinite-Dimensional Vector Spaces

    1. Front Matter
      Pages 213-213
    2. Sadri Hassani
      Pages 215-239
    3. Sadri Hassani
      Pages 241-263
    4. Sadri Hassani
      Pages 265-292
  5. Complex Analysis

    1. Front Matter
      Pages 293-293
    2. Sadri Hassani
      Pages 295-337
    3. Sadri Hassani
      Pages 339-361
    4. Sadri Hassani
      Pages 363-392
  6. Differential Equations

    1. Front Matter
      Pages 393-393
    2. Sadri Hassani
      Pages 417-457
    3. Sadri Hassani
      Pages 459-491
  7. Operators on Hilbert Spaces

    1. Front Matter
      Pages 509-509
    2. Sadri Hassani
      Pages 511-541
    3. Sadri Hassani
      Pages 543-561
    4. Sadri Hassani
      Pages 563-602
  8. Green’s Functions

    1. Front Matter
      Pages 603-603
    2. Sadri Hassani
      Pages 605-634
  9. Groups and Their Representations

    1. Front Matter
      Pages 699-699
    2. Sadri Hassani
      Pages 701-723
    3. Sadri Hassani
      Pages 725-760
    4. Sadri Hassani
      Pages 761-777
  10. Tensors and Manifolds

    1. Front Matter
      Pages 779-779
    2. Sadri Hassani
      Pages 781-827
    3. Sadri Hassani
      Pages 829-857
    4. Sadri Hassani
      Pages 859-911
  11. Lie Groups and Their Applications

    1. Front Matter
      Pages 913-913
    2. Sadri Hassani
      Pages 915-951
    3. Sadri Hassani
      Pages 953-985
    4. Sadri Hassani
      Pages 987-1007
    5. Sadri Hassani
      Pages 1009-1045
  12. Fiber Bundles

    1. Front Matter
      Pages 1077-1077
    2. Sadri Hassani
      Pages 1079-1098
    3. Sadri Hassani
      Pages 1099-1115
    4. Sadri Hassani
      Pages 1117-1141
    5. Sadri Hassani
      Pages 1143-1177
  13. Back Matter
    Pages 1179-1205

About this book

Introduction

The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex 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 edition 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 edition, 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."

Authors and affiliations

  • Sadri Hassani
    • 1
  1. 1.Illinois State University Department of PhysicsNormalUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01195-0
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-01194-3
  • Online ISBN 978-3-319-01195-0
  • Buy this book on publisher's site