Skip to content
Register Sign in Wishlist

The Geometry of Physics
An Introduction

3rd Edition


  • Date Published: November 2011
  • availability: Available
  • format: Paperback
  • isbn: 9781107602601

£ 60.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.

    • Develops geometric intuition
    • Presents physical applications
    • Highly readable and includes over 200 exercises
    Read more

    Reviews & endorsements

    Review of previous edition: '… highly readable and enjoyable … The book will make an excellent course text or self-study manual for this interesting subject.' Physics Today

    Review of previous edition: 'This book provides a highly detailed account of the intricacies involved in considering geometrical concepts.' Contemporary Physics

    'If you're looking for a well-written and well-motivated introduction to differential geometry, this one looks hard to beat.' Fernando Q. Gouvêa, MAA Online

    '… a first rate introductory textbook … the style is lively and exposition is clear which make the text easy to read … This book will be beneficial to students and scientists wishing to learn the foundations of differential geometry and algebraic topology as well as geometric formulations of modern physical theories.' Pure and Applied Geophysics

    '… this book should not be missing in any physics or mathematics library.' European Mathematical Society

    'This book is a great read and has a lot to offer to graduate students in both mathematics and physics. I wish I had had it on my desk when I began studying geometry.' AMS Review

    Review of previous edition: 'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt für Mathematik und ihre Grenzgebiete

    '… contains a wealth of interesting material for both the beginning and the advanced levels. The writing may feel informal but it is precise - a masterful exposition. Users of this 'introduction' will be well prepared for further study of differential geometry and its use in physics and engineering … As did earlier editions, this third edition will continue to promote the language with which mathematicians and scientists can communicate.' Jay P. Fillmore, SIAM Review

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Edition: 3rd Edition
    • Date Published: November 2011
    • format: Paperback
    • isbn: 9781107602601
    • length: 748 pages
    • dimensions: 248 x 174 x 33 mm
    • weight: 1.44kg
    • contains: 260 b/w illus. 205 exercises
    • availability: Available
  • Table of Contents

    Preface to the Third Edition
    Preface to the Second Edition
    Preface to the revised printing
    Preface to the First Edition
    Part I. Manifolds, Tensors, and Exterior Forms:
    1. Manifolds and vector fields
    2. Tensors and exterior forms
    3. Integration of differential forms
    4. The Lie derivative
    5. The Poincaré Lemma and potentials
    6. Holonomic and nonholonomic constraints
    Part II. Geometry and Topology:
    7. R3 and Minkowski space
    8. The geometry of surfaces in R3
    9. Covariant differentiation and curvature
    10. Geodesics
    11. Relativity, tensors, and curvature
    12. Curvature and topology: Synge's theorem
    13. Betti numbers and De Rham's theorem
    14. Harmonic forms
    Part III. Lie Groups, Bundles, and Chern Forms:
    15. Lie groups
    16. Vector bundles in geometry and physics
    17. Fiber bundles, Gauss–Bonnet, and topological quantization
    18. Connections and associated bundles
    19. The Dirac equation
    20. Yang–Mills fields
    21. Betti numbers and covering spaces
    22. Chern forms and homotopy groups
    Appendix A. Forms in continuum mechanics
    Appendix B. Harmonic chains and Kirchhoff's circuit laws
    Appendix C. Symmetries, quarks, and Meson masses
    Appendix D. Representations and hyperelastic bodies
    Appendix E. Orbits and Morse–Bott theory in compact Lie groups.

  • Resources for

    The Geometry of Physics

    Theodore Frankel

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact

  • Author

    Theodore Frankel, University of California, San Diego
    Theodore Frankel received his PhD from the University of California, Berkeley. He is currently Emeritus Professor of Mathematics at the University of California, San Diego.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.