As other authors of science blogs have pointed out: Most popular search terms are submitted by students. So I guess it is not the general public who is interested in: the *theory of gyroscopes*, *(theory of) microwaves, (theory of) heat pumps,* *(theory of) falling slinkies*, or the *Coriolis force*.

I believe that these search terms are submitted by students in physics or engineering.

**“Student Friendly Quantum Field Theory” has been the top search term for this blog** since I had put the textbook of the same title by Robert Klauber on my physics resources list.

So I pay my dues now and dedicate a post to this textbook: I am reviewing the first edition 2013, as I have just missed the publication of the 2nd. In short: I think the book is a pedagogical masterpiece.

This is also an auxiliary posting in my series on QFT. I want to keep this post to a reasonable non-technical level not to scare off my typical readers too much (but I apologize for some technical terms – having the “target audience” of physics students in mind).

*Quantum field theory for the gifted amateur* has been searched for as well. I believe indeed that this is a book for the *gifted amateur *in terms of a self-studying quantum physics enthusiast, at least more so than other books on QFT.

However, also the amateur should have had a thorough education in theoretical physics. If you have mastered your typical [*] four (?) semesters in theoretical physics – classical mechanics, electrodynamics, (non-relativistic) quantum theory, and statistical mechanics you should be well prepared to understand the material in this book. If the following key words trigger some memories of equations, you meet the requirements: *Lagrange formalism of classical mechanics, Poisson bracket, Maxwell’s equations in four-vector notation.*

[*] I have graduated at a time when bachelor’s degrees have been unheard of here in Europe – I cannot explain the prerequisites properly in terms of modern curricula or “graduate” versus “undergraduate”.

I had some exposure to quantum field theory that is used in solid state physics, too, but I don’t believe this is a pre-requisite.

I was most interested in a thorough understanding of the basics and less so in an elegant discussion of leading-edge theories. As discussed in detail earlier I can track down exactly when I don’t understand popular physics books – and by “understanding” I mean being able to recognize the math behind a popular text. (However, in this sense pop-sci books can be definition not be “understood” by the lay audience they are written for).

I didn’t have an idea how the Higgs boson gives the particles and mass, and I could not image how the electron’s spin could be a by-product yielded by a theory – so I wanted to plow through the foundations of QFT. If you want to understand the Higgs boson and field, too, this book does not yet explain this – but I believe you need some thorough grounding as given by SFQFT if you want to tackle more advanced texts.

We don’t learn much about Robert Klauber himself. The blurb says:

Bob Klauber, PhD, is retired from a career of working in industry, where he led various research projects and obtained over twenty patents. At different times during and after that career, he taught a diverse number of graduate and undergraduate level physics courses.

So the author is not a tenured professor, and I believe this might be advantageous.

**Written solely for students, not for peers**

Klauber does not need to show off his smartness to his peers. Yes, he has some pet peeves – such as questioning the true nature of the vacuum, often painted in popular science as a violent sea consisting of pairs of particles popping out of nowhere and vanishing again. Klauber tags some opinions of his as non-mainstream [**], and he links to a few related papers of his own – but he does so in a rather humble way. Your milage may vary but I found it very refreshing not to find allusions to the impact and grandness of this own original work or to his connectedness in the scientific community (in terms of …*when I occasionally talked to Stephen Hawking last time at That Important Conference…)
*[**] I feel the need to add a disclaimer: This is not at all “outsider physics” or unorthodox in the way the term is used by professionals bombarded with questionable manuscripts by authors set to refute Einstein or Newton.

But it is not an “elegant” book either. It is not providing professionals with “new ways to see QFT as you never saw it before”; it is an anti-Feynman-y book so to speak. It is not a book I would describe in the way the publishers of the Commemorative Issue of Feynman’s Physics Lectures (1989) did:

Rereading the books, one sometimes seems to catch Feynman looking over his shoulder, not at his audience, but directly at his colleagues, saying, “Look at that! Look how I finessed that point! Wasn’t that clever?”

**Nothing is Trivial, Easy and Obvious – and brevity is avoided
**

Student Friendly Quantum Field Theory (SFQFT) is dedicated to tackling the subject from the perspective of the learning student primarily and only. Klauber goes to great lengths to anticipate questions that might be on the reader’s mind and often refers to his own learning experience – and he always perfectly nails it. He explicitly utters his contempt for declaring things trivial or straight-forward.

Klauber has put considerable efforts into developing the perfect way(s) of presenting the material. Read a summary of his pedagogical strategy here. He avoids conciseness and brevity and he wonders why these seem to be held in such high regard – in education. This also explains why a book of more than 500 pages covers basics only. The same ideas are expounded in different forms:

- Summary upfront, “big picture”.
- Through derivations. In case of renormalization, he also gives sort of a “detailed overview” version in a single chapter before the theory unfolds in several chapters. The structure of the book is fractal so to speak: There are whole chapters dedicated to an overview – such as Bird’s Eye View given in Ch. 1 or the summary chapter on renormalization, and each chapter and section contains their own summaries, too.
- So-called
*Wholeness Charts*, tabular representations of steps in derivations. I found also the charts in the first chapters extremely useful that allow for comparing non-relativistic QM and QFT, and between “particle QM” and field theory – I owe Klauber for finally clearing up my personal confusions – since I haven’t noticed before that I had been trained in non-relativistic field theories. The summary of major steps in the development of the theory for different kinds of particles are laid out in three columns of a table covering several pages, one for each type of particle. - Another Summary the the end.

**Nothing is omitted (The ugly truth).
**

The downside:

Now I have understood why Dirac called this an ugly theory he refused to consider the final fundamental theory of the universe. Klauber gives you all the unwieldy algebra. I have not seen something as ugly and messy as the derivations of renormalization. The book has about 520 pages: 100 of them are dedicated to renormalization, and 85 to the calculation of cross-sections in order to compare them with experiment.

The good things:

Klauber gives you really all the derivations, not a single step is omitted. Very often equations quoted in earlier chapters are repeated *for convenience of the reader*. The book contains problems, but none of the derivations essential for grasping new concepts are completely outsourced to the problems sections.

**Scope of the book**

You can read the first chapters of the book online, and here is the Table of Contents.

Klauber suspects the addition of modern theories and applications would be confusing and I believe he is right.

He starts with the **relation of QFT and non-relativistic and/or non-field-y quantum physics. **I like his penchant for the Poisson bracket in particular and the thorough distinction between wave functions and fields, and how and if there is a correspondence. Take this with a grain of salt as I had been confused a lot with an older book that referred to anything – Schrödinger wave function as well as field – as “waves”.

Klauber uses quantum electrodynamics as the example for explaining concepts. Thus he follows the historical route approximately, and he quotes Feynman who stated that he always thought about theories in terms of palpable examples.

The table of contents is rather “orthodox”.

**Free fields are covered first and related equations for scalar bosons (the simplest example), fermions and vector bosons.** The latter are needed as ingredients of QED – electrons and photons. I enjoyed the subtle remarks about over-emphasizing the comparison with harmonic oscillators.

Field equations for fermions (such as electrons) do not have classical counter-parts – this is where all attempts to explain by metaphor must end. I set out to write a pop-sci series on QFT and accidentally read the chapter on fermions at the same time when David Yerle posted this challenge on his blog – how to explain the electron’s spin: Now I believe there is no shortcut to understanding the electron’s spin – and as far as I recall Richard Feynman and Sean Carroll (my benchmarks in terms of providing correct popularizations) weren’t able to really explain the electron’s spin in popular terms either. There are different ways to start from but these field equations don’t have classical counterpart, and you always end up with introducing or “discovering” mathematical objects that behave in an non-intuitive way – “objects” that anti-commute without being equal to zero (There aren’t any numbers A and B that satisfy AB = -BA unless either A or B are zero).

**Interactions**are introduced via Maxwell’s equations and QED. Inspecting these equations we finally learn how symmetry and forces are related – usually cloaked as

*symmetry gives rise to forces*in popular texts. Actually, this was one of the things I was most interested in and it was a bit hard to plow through the chapter on spinors (structures representing electrons) before getting to that point.

**Symmetry** is covered in two chapters – first for free fields and then for interacting fields. All that popular talk about rotating crystals etc. will rather not explain what Gauge Symmetry really is. Again I come to the conclusion that using QED (and the Lagrangian associated with Maxwell’s equation) as an example is the right thing to do, but I will need to re-read other accounts that introduce interacti0ns immediately after having explained scalar b0s0ns.

The way Feynman, Schwinger and Tomonaga **dealt with infinities via renormalization is introduced after the chapter on interactions**. Since this is the first time I learned about renormalization in detail it is difficult to comment on the quality. But I tend to agree with Klauber who states that students typically get lost in these extremely lengthy derivations that include many side-tracks. Klauber tries to keep it somewhat neat by giving an overview first – explaining the strategy of these iterations (answering: *What the hell is going on here?*) and digging deeper in the next chapters.

Applications are emphasized, so we learn about the daunting way of **calculating scattering cross-sections to be compared with experiments**. Caveat: Applications refer to particle physics, not to solid-state physics – but this was exactly what I, as a former condensed matter physicist, was looking for.

Klauber uses the canonical quantization that I had tried to introduce in my series on QFT, too (though I tried to avoid the term). Nevertheless, at the end of the book a **self-contained introduction to path integrals** is given, too, and part of it is available online.

In summary I wholeheartedly recommend this book to any QFT newbie who is struggling with conciser texts. But I am not a professional, haven’t read all QFT books in the world and my requirements as a student are probably peculiar ones.