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Differential Geometry and Lie Groups for Physicists 1st Edition

6 customer reviews
ISBN-13: 978-0521845076
ISBN-10: 0521845076
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Editorial Reviews


"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."
Hans-Peter Künzle, Mathematical Reviews

"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

"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

"... 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

"Marián Fecko deftly guides you through the material step-by-step, with all the rigor, 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."
Sergei Slobodov, UBC for Physics in Canada

Book Description

Covering subjects including manifolds, tensor fields, spinors, and differential forms, this 2006 textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.


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Product Details

  • Hardcover: 714 pages
  • Publisher: Cambridge University Press; 1 edition (October 30, 2006)
  • Language: English
  • ISBN-10: 0521845076
  • ISBN-13: 978-0521845076
  • Product Dimensions: 6.8 x 1.5 x 9.7 inches
  • Shipping Weight: 3.4 pounds (View shipping rates and policies)
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #4,326,018 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

12 of 15 people found the following review helpful By TreeTiger on July 15, 2008
Format: Hardcover
There's no doubt about it: the material in this book is incredibly interesting and important for an ambitious physics student. The organization of the book is fairly good: informal passages relating the necessary theory alternate with exercises which are all written as "Check that..." or "Prove that...", which allows you to choose which results to prove and which to take as given facts if you -- for any reason -- don't feel like proving them.

However, the book also has some serious shortcomings. The most important one seems to be the horrid style. A book of mathematics for physicists should not be written just like a standard math textbook without proofs -- and this is exactly what this book is like. The definitions that are given are "mathematical" at heart; very rarely can one find an intuitive picture of what is going on immediately after a concept is introduced. On the other hand, the propositions that are not left as excercises are never proven. Granted, they might be intuitively clear, but that doesn't mean that their proofs are obvious. Due to all this, I have always felt a bit confused and certainly not comfortable with new concepts. The author's occasional attempts to "raise morale" by inserting jokes would always backfire because these jokes are so trivial that they seem offensively condecending. Take, for example, the sentence that finishes the introduction of a vector as the equivalence class of tangency of curves:

"And a good old arrow, which cannot be thought of apart from the vector, could be put at P in the direction of this bunch, too (so that it does not feel sick at heart that it had been forgotten because of some dubious novelties)." (p. 25)

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17 of 23 people found the following review helpful By Z. Tan on March 26, 2007
Format: Hardcover
The book covers a good range of topics in Differnetial geometry with lots of exercises. One literarily has to do the exercises to develop the concept. Ecah chapter ends with a concise summary of the key equations. The problem is that all the exercises are mixed with the main context. It lacks any exposition or concept development for most of the topics, no definition, no prove, and every page is filled with exercises. This style make it difficult for someone to learn the subjects the first time or to use it as a reference.

Separately, there are too few graphs to assist the reader to visualize the ideas. The prints are also small making it hard to read.

Nakahara's book (Geometry, topology and physics) is a much better choice on the same subject.
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6 of 8 people found the following review helpful By Michal Tarana on July 21, 2007
Format: Hardcover
Marian Fecko's textbook covers well fundamental elements of modern differential geometry and introduction to the Lie groups (not only) from geometrical point of view. Geometrical formulations of the classical mechanics, gauge theory and classical electrodynamics are discussed.

The textbook expects the reader to be familiar with mathematical analysis on the level of the standard course usual in the physics undergraduate study programs. Understanding of the parts dealing with physical applications (classical mechanics and electrodynamics) expects knowledge of fundamental principles of these subjects. Organization of the book allows the reader to concern on particular part, i. e. understanding of later parts doesn't require reading of all previous parts (reading of parts concerning on the classical dynamics does not require reading of parts dealing with electrodynamics). However, relations between different subjects of the theory are explained instructively.

The main advantage of this textbook is that reader "builds" the subject himself by solving the exercises usually appended by hints. It makes all the elements of the theory natural to the reader during study. This way is a little bit more time consuming when compared with other textbooks dealing with this subject. It provides good starting point for study of mathematical aspects of the general relativity and field theories. I recommend this book to everybody who wants to understand fundamental concepts in differential geometry in detail.
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Differential Geometry and Lie Groups for Physicists
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