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).
154 black & white illustrations, 15 blac
154 black & white illustrations, 15 blac
Most Helpful Customer Reviews
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...
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...
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