You can read my review at https://www.amazon.com/Quantum-Fiel...623/ref=sr_1_1?ie=UTF8&qid=1316208079&sr=8-1"(adsbygoogle = window.adsbygoogle || []).push({});

What follows is a copy:

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. For instance, the double arrow symbol meaning "implies" is used to indicate mappings. The vocabulary is different. For instance, single-valued is used to mean one-to-one, and repulsive force is used to mean restorative force. The definitions are different. For instance the Laplace transform is different from the standard one used by both mathematicians and physicists.

There are assymetries in the text that are inexplicable from any point of view. To denote the dual space of a linear space one finds a superscripted d, asterisk, or prime depending on the page number. Variables that commute are commuted in the middle of a derivation without any reason. What are we to make of the first page of the preface to the first volume? Are we to understand that the gravitational and electromagnetic forces are not between elementary particles but that the strong and weak forces are?

The typos come hot and heavy. Professor Zeidler is not a native speaker of English and you would think that he would have the book proof-read by someone who was. There are too many spelling and grammatical errors for that to be the case. For that matter, he doesn't seem to be a native speaker of the mathematical language either and that is a major problem because of the purpose of the book. Typos in the equations are depressingly common and the figures are wrong too. Figure 5.7b on page 234 of volume I subtracts 1000 words from the discussion it illustrates because one of the arrows points in the wrong direction. Figure 8.1b on page 700 of vol II is truly breathtaking as it depicts a comet being repelled by the gravitational force of the sun.

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# Zeidler, QFT: A Bridge between Mathematicians and Physicists.

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