Topics in Physical Mathematics

  • Kishore Marathe

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Kishore Marathe
    Pages 1-32
  3. Kishore Marathe
    Pages 33-71
  4. Kishore Marathe
    Pages 73-105
  5. Kishore Marathe
    Pages 107-136
  6. Kishore Marathe
    Pages 137-167
  7. Kishore Marathe
    Pages 169-206
  8. Kishore Marathe
    Pages 207-234
  9. Kishore Marathe
    Pages 235-274
  10. Kishore Marathe
    Pages 275-312
  11. Kishore Marathe
    Pages 313-350
  12. Kishore Marathe
    Pages 351-375
  13. Back Matter
    Pages 377-442

About this book

Introduction

The roots of ’physical mathematics’ can be traced back to the very beginning of man's attempts to understand nature. Indeed, mathematics and physics were part of what was called natural philosophy. Rapid growth of the physical sciences, aided by technological progress and increasing abstraction in mathematical research, caused a separation of the sciences and mathematics in the 20th century. Physicists’ methods were often rejected by mathematicians as imprecise, and mathematicians’ approach to physical theories was not understood by the physicists. However, two fundamental physical theories, relativity and quantum theory, influenced new developments in geometry, functional analysis and group theory. The relation of Yang-Mills theory to the theory of connections in a fiber bundle discovered in the early 1980s has paid rich dividends to the geometric topology of low dimensional manifolds. Aimed at a wide audience, this self-contained book includes a detailed background from both mathematics and theoretical physics to enable a deeper understanding of the role that physical theories play in mathematics. Whilst the field continues to expand rapidly, it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader to their next point of exploration in this vast and exciting landscape.

Keywords

Theoretical physics classical and quantum field theories differential geometry and topology invariants of 3- and 4-dimensional manifolds manifold mathematical physics physical mathematics ring theory

Authors and affiliations

  • Kishore Marathe
    • 1
  1. 1.Brooklyn CollegeCity University of New YorkBrooklynUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84882-939-8
  • Copyright Information Springer-Verlag London Limited 2010
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84882-938-1
  • Online ISBN 978-1-84882-939-8
  • About this book