Skip to content
Register Sign in Wishlist

Differential Geometry and Lie Groups for Physicists

£56.99

  • Date Published: March 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521187961

£ 56.99
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback, eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.

    • Complex ideas or computations are divided into a sequence of simple and clear statements which can then be easily grasped
    • Much of the theory is illustrated through simple exercises (over 1000 altogether), with detailed hints
    • End-of-chapter summaries give important concepts, results and formulas
    • Uses both standard mathematical and physical terminology, building a bridge between the jargons involved
    Read more

    Reviews & endorsements

    Review of the hardback: 'All basic material that is necessary for a young scientist in the field of geometrical formulation of physical theories is included … ordered and represented in a very appropriate manner … with a great respect to the reader. … I truly believe that reading this book will bring a real pleasure to all physically inclined young mathematicians and mathematically inclined young physicists … a very good high level textbook … [I] recommend it to all young scientists being interested in finding correspondence between harmony in the physical world and harmony in geometrical structures. … well written, very well ordered and the exposition is very clear.' Journal of Geometry and Symmetry in Physics

    Review of the hardback: 'the contents of this book covers a lot (if not most) of what a theoretical physicist might wish to know about differential geometry and Lie groups. particularly useful may be that the modern formalism is always related to the classical one with tensor indices still mostly used in the physics literature.' American Mathematical Society

    Review of the hardback: '… the presentation is almost colloquial and this makes reading rather pleasant. The author has made a concerted effort to give intuitive interpretations of complicated ideas such as: the Lie derivative, tensors, the Hodge star operator, Lie group representations, Hamiltonian and Lagrangian mechanics, parallel transport, connections, curvature, gauge theories, spinors and Dirac operators. This will be much appreciated by students (and even researchers, I think). … an excellent reference for geometers.' Zentralblatt MATH

    Review of the hardback: 'The contents of this book cover a lot (if not most) of what a theoretical physicist might wish to know about differential geometry and Lie groups.' Mathematical Reviews Hans-Peter Künzle

    Review of the hardback: 'Marian Fecko deftly guides you through the material step-by-step, with all the rigour, but without the pain. When going through the chapters, definition by definition, proof by proof and hint by hint, you get an impression of a caring, experienced (and often quirkily funny, but never boring) tutor who really, really wants you to succeed.' Physics in Canada

    Review of the hardback: 'From the point of view of presentation the book has a lot going for it. It is written in a pedagogically discursive, conversational style with numerous workable examples and exercises distributed through the text. … From the UK perspective a student undertaking a level 4 (level 5 in Scotland) or MSc course in theoretical physics would find this book well-pitched to his or her needs.' Contemporary Physics

    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

    • Date Published: March 2011
    • format: Paperback
    • isbn: 9780521187961
    • length: 714 pages
    • dimensions: 244 x 170 x 36 mm
    • weight: 1.12kg
    • availability: Available
  • Table of Contents

    Introduction
    1. The concept of a manifold
    2. Vector and tensor fields
    3. Mappings of tensors induced by mappings of manifolds
    4. Lie derivative
    5. Exterior algebra
    6. Differential calculus of forms
    7. Integral calculus of forms
    8. Particular cases and applications of Stoke's Theorem
    9. Poincaré Lemma and cohomologies
    10. Lie Groups - basic facts
    11. Differential geometry of Lie Groups
    12. Representations of Lie Groups and Lie Algebras
    13. Actions of Lie Groups and Lie Algebras on manifolds
    14. Hamiltonian mechanics and symplectic manifolds
    15. Parallel transport and linear connection on M
    16. Field theory and the language of forms
    17. Differential geometry on TM and T*M
    18. Hamiltonian and Lagrangian equations
    19. Linear connection and the frame bundle
    20. Connection on a principal G-bundle
    21. Gauge theories and connections
    22. Spinor fields and Dirac operator
    Appendices
    Bibliography
    Index.

  • Author

    Marián Fecko, Comenius University, Bratislava

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

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

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 www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

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.

Cancel

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.
×