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Quantum Field Theory I: Basics in Mathematics and Physics: A Bridge between Mathematicians and Physicists (v. 1) 1st.ed. 2006. Corr. 2nd printing 2009 Edition

3.6 out of 5 stars 5 customer reviews
ISBN-13: 978-3540347620
ISBN-10: 3540347623
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Editorial Reviews

Review

From the reviews:

"Quantum field theory combines relativity, quantum mechanics, and many-particle physics to provide a theoretical basis for the most fundamental understanding of our universe. … it is a fun book for practicing quantum field theorists to browse, and it may be similarly enjoyed by mathematical colleagues. Its ultimate value may lie in encouraging students to enter this challenging interdisciplinary area of mathematics and physics. Summing Up: Recommended. Upper-division undergraduates through faculty." (M. C. Ogilvie, CHOICE, Vol. 44 (9), May, 2007)

"This is the first volume of a six volume book on quantum field theory. … The main object is to explain mathematics for students or researchers in physics how to use them, and to show students and researchers in mathematics how to use them, and to show students and researchers in mathematics how to use mathematics in physics. Translations of different languages used by mathematicians and physicists for the same mathematical objects are also presented." (Akira Asada, Zentralblatt MATH, Vol. 1124 (1), 2008)

"This book on quantum field theory, consisting of over a thousand pages, is the first volume of a projected six-volume series. It alone has seventeen chapters and an appendix … . The appendix covers notation, units, and dimensional analysis. … Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from other books on quantum field theory in its greater emphasis on the interaction of physics with mathematics. … an impressive work of scholarship." (William G. Faris, SIAM Review, Vol. 50 (2), 2008)

“Volume I is divided in three parts. Part 1 has an introductory nature. … Part II accompanies the reader through a forest of basic techniques in mathematics. … In Part III, Zeidler presents the essential available information on heuristic magic formulas of quantum field theory. … The presentation of the material is clear. … For a scholar aiming to work in quantum field theory … Zeidler can be a reference text. … Mathematicians can find a list of topics who are still waiting rigorous treatments.” (Paolo Maria Mariano, Meccanica, Vol. 46, 2011)

From the Back Cover

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction).

From the reviews:

"… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from other books on quantum field theory in its greater emphasis on the interaction of physics with mathematics. … an impressive work of scholarship."

(William G. Faris, SIAM Review, Vol. 50 (2), 2008)

 "… it is a fun book for practicing quantum field theorists to browse, and it may be similarly enjoyed by mathematical colleagues. Its ultimate value may lie in encouraging students to enter this challenging interdisciplinary area of mathematics and physics. Summing Up: Recommended. Upper-division undergraduates through faculty."

(M. C. Ogilvie, CHOICE, Vol. 44 (9), May, 2007)

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Product Details

  • Hardcover: 1052 pages
  • Publisher: Springer; 1st.ed. 2006. Corr. 2nd printing 2009 edition (April 6, 2011)
  • Language: English
  • ISBN-10: 3540347623
  • ISBN-13: 978-3540347620
  • Product Dimensions: 6.1 x 2.2 x 9.2 inches
  • Shipping Weight: 3.5 pounds (View shipping rates and policies)
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #2,008,816 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on October 24, 2009
Format: Hardcover Verified Purchase
If is not too unfair to say that quantum field theory is a kind of bag of tricks, but considering its monumental experimental success it is apparent that these tricks have worked. From a mathematical standpoint they are very suspect, and the professional mathematician who studies the formalism of quantum field theory will be aghast at its non-rigor, especially in the area of renormalization. That is not to say that no attempts have been made to put quantum field theory on a rigorous mathematical foundation. This has occupied the time of many researchers, but as of yet, such a foundation has not been found.

In spite of this, and justifiably so, quantum field theory goes on, and people taking up its study are faced at times with making choices between mathematical rigor and physical relevance. The author of this book, the first of a planned series of 4 volumes, realizes this and has attempted to give the reader a first glance of quantum field theory that emphasizes both the physics and the mathematical relationships that are part of its narrative. In general the author does a fairly good job, even though at times the details of certain subjects are left out, while others are developed to excess.

From selective chapters, this reviewer found that the following discussions stand out:

A Glance at Topology:
This chapter does not contain a whole lot of insights or material that cannot be found in other books. The author it seems wants to whet the reader's appetite but clearly wants to put off detailed discussion of the mathematics until Volume 3 or 4 of this series.
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Format: Hardcover
I'm in love with QFT. I noticed this planned monumental 6-volume work some time ago but I bought this book from Amazon UK after reading Quantum Field Theory Demystified and looking for more thorough ab initio treatment of QFT. Upon its arrival I immersed myself into it and in my opinion the first volume is like The Road to Reality book but more mathematically oriented with proofs, numerous examples, historical notes, generous citations and references.

Thanks,
Dmitry Vostokov
Founder of Literate Scientist Blog
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Format: Hardcover Verified Purchase
Whenever I read a book on quantum field theory, I have felt that there are something missing. This is not the faults by the authors. Since the QFT is widely used in most fields of physics, it should be limited in writing such a book. It is believed to be impossible for writing a complete book on the QFT in its various aspects.

In my institution, I was enforced to give several lectures on solid states physics to whom have no knowledge on quantum physics, of course, they have no knowledge on Hamiltonian physics neither. The undergraduate background of the students are very diversified, from mathematics to engineering. There Ph.D. major will not be Physis, certainly. I spent many years with nightmare for preparing those lecture courses. Working as a computational physicist in an engineering school could not be a recommended choice! For several years, I have tried to step outside the QFT for living.

During my struggling to absorb the strange way of thinking by metallurgists, I noticed a way to tackle dislocations in the line with the approach suggested by Stephen Hawking for black holes armed with homotopy. I rushed to my bookshelves and to pick up a book of Dirac on the general theory of relativity as well as the QFT books, e.g., Bjorken & Drell, Fetter & Walecka, and Negele&Orldando. In addition, the book of Zinn-Justine and of P. W. Anderson are always helpful. Those books awoke my interests in the QFT. I also bought a couple of books on the QFT in the curved spacetime. I just read them at a glance and I confirmed my idea. The required methods are there in. Unfortunately, I am not an expert in these fields: Kohn-Sham equation is my best field. In order to show up the results of my idea, I need a very systematically written book on QFT, especially with emphasis in mathematics.
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Format: Hardcover Verified Purchase
I have the second (2009) printing of volume I, and the first printing (2008) of volume II of this book. Page numbers may differ if you have different printings.

I fear that I cannot say enough bad things about this book in the short space of this review. According to the author physicists need to extend their methods further than can be justified by rigorous mathematics. In such cases formal methods are used. On the other hand, mathematicians have strayed away from the kinds of intuitive insights that come from solving problems in the physical world. Why isn't there more cooperation? Because they don't speak the same language. These books are intended as a bridge between mathematicians and physicists. The reader would expect at least some translation between the two languages and sure enough, on page 332 of Vol II, such a lexicon exists. In it there are 5 examples. For instance, what is called a connection in mathematics is called potential in physics. That's it, 5 translations. If only physicists and mathematicians were aware of these 5 translations the channels of communication would be opened up and the mathematicians could find rigorous proofs of the methods used by the physicists.

It is not made clear how the other 6000 (I'm extrapolating) pages of the book form a bridge. One idea presented is that when rigorous math can only take you so far, you must use heuristic, or formal methods. However, mathematical rigor is not defined and examples of it are not given. The reader may not know what the author is talking about. One problem in this regard is that the author sometimes uses formal arguments even when rigorous mathematical methods already exist.

The material is presented in a way that is foreign to both mathematicians and physicists. The notation is different.
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