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Quantum Field Theory III: Gauge Theory: A Bridge between Mathematicians and Physicists Hardcover – August 17, 2011

ISBN-13: 978-3642224201 ISBN-10: 3642224202 Edition: 2011th

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Quantum Field Theory III: Gauge Theory: A Bridge between Mathematicians and Physicists + Quantum Field Theory II: Quantum Electrodynamics: A Bridge between Mathematicians and Physicists + Quantum Field Theory I: Basics in Mathematics and Physics: A Bridge between Mathematicians and Physicists (v. 1)
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Product Details

  • Hardcover: 1126 pages
  • Publisher: Springer; 2011 edition (August 17, 2011)
  • Language: English
  • ISBN-10: 3642224202
  • ISBN-13: 978-3642224201
  • Product Dimensions: 2.7 x 6.5 x 9.8 inches
  • Shipping Weight: 3.8 pounds (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #688,778 in Books (See Top 100 in Books)

Editorial Reviews


From the reviews:

“This book is the third volume of a complete exposition of the important mathematical methods used in modern quantum field theory. It presents the very basic formalism, important results, and the most recent advances emphasizing the applications to gauge theory. … the book’s greatest strength is Zeidler’s zeal to help students understand fundamental mathematics better. I thus find the book extremely useful since it signifies the role of mathematics for the road to reality … .” (Gert Roepstorff, Zentralblatt MATH, Vol. 1228, 2012)

“The present book is a good companion to the literature on the subject of the volume title, especially for those already familiar with it. … the book touches upon a large number of subjects on the interface between mathematics and physics, providing a good overview of gauge theory in both fields. It contains lots of background material, many historical remarks, and an extensive bibliography that helps the interested reader to continue his or her more thorough studies elsewhere.” (Walter D. van Suijlekom, Mathematical Reviews, Issue 2012 m)

From the Back Cover

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction.


Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure.


The book is arranged in four sections, devoted to realizing the universal principle force equals curvature:


Part I: The Euclidean Manifold as a Paradigm

Part II: Ariadne's Thread in Gauge Theory

Part III: Einstein's Theory of Special Relativity

Part IV: Ariadne's Thread in Cohomology


For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum.


Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

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Most Helpful Customer Reviews

17 of 20 people found the following review helpful By A Reader on October 18, 2011
Format: Hardcover Verified Purchase
This is not a review of the contents of Dr. Zeidler's book; I simply wish to question Springer-Verlag's choice of binding for Volume III in this projected series and bring a concern to the attention of prospective buyers.

The hardbound editions of Volumes I and II in this series were bound in identical (and attractive) covers and came clearly labeled as Quantum Field Theory I and Quantum Field Theory II on the spines. However, Volume III is bound in an entirely different style, and the identifying label on the spine is printed so differently from Volumes I and II that the third volume does not even appear to be part of the same series. As I said in the title of this review, this is indeed a "cosmetic" concern, but when one is investing several hundred dollars in an ambitious series like this, the least one can expect is continuity and coherence in the binding and cover design.

This issue will surely not deter any serious reader from purchasing this unique and ambitious series. However, one cannot detect the difference through online views of the books; I thought that prospective buyers should at least be aware of the problem. I now wonder what the future volumes in this series will look like.
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4 of 16 people found the following review helpful By James M. Snyder on December 21, 2011
Format: Hardcover Verified Purchase
Regardless of any subjective reasons for liking this book, there is an objective reason for rejecting it and sending it back to the author for revision. The problem lies in the notation used for change of variables. There is a standard notation for it, used by mathematicians and physicists alike. One may look at the wiki entry for "Tensor" for comparison. However, the author uses instead a non-standard one. This would not be a problem if the author's notation were an improvement, or at least as good as the standard, or even just a little bit worse, but it is not.

The problem can be first seen in eqn (0.35), page 24. Here we see what appears to be a distinction being made between two different dummy variables. However, that is not the meaning that the author intends. He means that the sum is invariant under a change of variables from x to x' = x'(x). In standard notation, the prime would be on the letter v and not on the index alpha. Delta needs to be carefully defined so that we know whether it is the partial with respect to x, or x'. As it is, it appears to be with respect to the alpha prime index on x, but in reality it is something quite different. This is not a typo as we see from the line just below the equation. Here we cannot fix things by removing the prime from the index alpha and placing it on the variable v for in doing so we would end up with three alpha indices on the right hand side of the equation rendering it meaningless. Moving down one more line we see primes on integer indices. One might wonder what 1', 2', 3' and 4' are meant to be. In fact they are, of course, 1, 2, 3, and 4.
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