The Mathematical Structure of Classical and Relativistic Physics

A General Classification Diagram

  • Enzo Tonti

Table of contents

  1. Front Matter
    Pages i-xxxvi
  2. Enzo Tonti
    Pages 1-18
  3. Analysis of Variables and Equations

    1. Front Matter
      Pages 19-19
    2. Enzo Tonti
      Pages 21-37
    3. Enzo Tonti
      Pages 63-87
    4. Enzo Tonti
      Pages 89-153
    5. Enzo Tonti
      Pages 155-179
    6. Enzo Tonti
      Pages 181-220
    7. Enzo Tonti
      Pages 221-238
  4. Analysis of Physical Theories

    1. Front Matter
      Pages 239-239
    2. Enzo Tonti
      Pages 241-271
    3. Enzo Tonti
      Pages 273-323
    4. Enzo Tonti
      Pages 325-354
    5. Enzo Tonti
      Pages 355-383
    6. Enzo Tonti
      Pages 385-412
  5. Advanced Analysis

    1. Front Matter
      Pages 413-413
    2. Enzo Tonti
      Pages 415-428
    3. Enzo Tonti
      Pages 429-455
  6. Back Matter
    Pages 457-514

About this book


The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence. Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows one to construct a classification diagram for variables, equations, and other theoretical characteristics.

The book is divided into three parts. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories.

Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Written at a level accessible to graduate and advanced undergraduate students in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework.


applied partial differential equations diffusion electromagnetism gravitation theory mathematical structure physical theories physical variables solid deformation thermal conduction

Authors and affiliations

  • Enzo Tonti
    • 1
  1. 1.Dept. of Engineering and ArchitectureUniversity of TriesteTriesteItaly

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7421-0
  • Online ISBN 978-1-4614-7422-7
  • Series Print ISSN 2164-3679
  • Series Online ISSN 2164-3725
  • Buy this book on publisher's site
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