Student-Friendly Quantum Field Theory Vol 1: At Last, Someone Gets It!

An experience that the vast majority of physics graduate students have all shared over the last 60 years or so is the shared excitement, challenge, and more often than not agony of taking a quantum field theory course. 

Most institutions (bar a few notable exceptions), ensures the first foray into QFT that a student encounters, is one which covers the canonical quantisation approach (over the more alien, yet more universally useful path integral approach).  

The most sensible approach (which, happenstance is the most centrally used) I have seen to date, is to begin with an advanced review of special relativity; an introduction to classical field theory; an overture of Noether symmetries; the Klein-Gordon Equation; Green's functions and propagators; the Dirac Equation; CPT symmetries, with the lecture series ending on the S-Matrix and calculation of Feynman rules (with the optional addition of quantum electrodynamics).

Accompanying such lecture courses, is a long list of mandatory exercise sheets to complete. As any modern age physicist would tell you (if not, certainly should know), the success of any student is: practice, practice and more practice. This is especially true in field theory research, where these difficult calculations are carried out on a day to day basis. 

It is then to the discredit of theoretical physics education that these sheets do not facilitate learning or promote understanding of the material. Brevity is the coarse sand which poisons the well in this case. Too often is the method of arriving at results or insights left to the wayside; in favour of vague and seemingly unconnected statements and results. 

As the old saying goes "the proof is in the pudding", and this pudding has certainly gone missing!

The frustration any serious student of QFT has faced, is the enormity of time spent on the dictation of the theory (and by equivalence mind-numbingly easy examples) within lectures; with the more difficult, useful and (to many a student's woes) more examinable content of the lecture course being relegated to "self study" in the exercise sheets themselves. It is within these question sheets, that students become demotivated, and in many cases puts them off field theory entirely.  

This issue has also imposed itself on many of the "popular" (mainly to researchers in the field) quantum field theory books. Often, textbooks (at least in the European and British standard of university teaching) are secondary sources of information (with the expectation that the lecturer's notes should be enough to digest and understand the material), a second opinion. As a point of issue, the QFT textbook has becomes less (though there exists a few notable exceptions to this) instructive. 

Though the vast majority of historical QFT textbooks are technically excellent, well written, and provide warm and close companionship along a researcher's career; to the student, such texts present a harrowingly similar presentation as those seen in the lectures, with the same or lesser detail.

Too often is the defence used: "students learning through struggling" or "They won't learning anything if you give them the answers".  On one hand, it is easy to see (and agree) wholly with these statements. Hard work should be a vital trait which we instil onto our students; and this "struggle" is a part of that.

However, to this I say, QFT is to all intents and purposes a practical, ever-changing field of study; it is the small intricate details seen in all their glory which lends to the student a crux, upon where they can build a foundation of understanding.

Student friendly Quantum Field Theory Volume 1 (2nd edition) by Robert  "Bob" D. Klauber is the leading antidote (alongside a few notable modern QFT textbooks) in tackling this Darwinian culture of QFT in physics education.

From the preface, Klauber outlines his pedagogy as a manifesto against all the problems stated above with the current literature. 

Klauber understands the student, more than the student understands themselves. This is evidenced by his inclusion of reviews of preceding topics  (such as quantum mechanics and special relativity) before they are needed in the following chapter . 

Klauber also includes wholeness charts throughout the text; along with annotation boxes outlining key ideas in the margin of the text at various points. This also helps to envision in the student minds the connections between various topics. 

The book covers the canonical quantisation approach for spin-0; spin-1; spin-1/2 quantum field theories; along with a quantum electrodynamics, renormalisation and regularisation. Moreover, there are many worked problems in the text, along with separate solution manual (available for students as well as instructors) for the end of chapter exercises. 

Disgruntled naysayers of this text (of which I’m sure there will be many) will be quick to point out that this text does not cover aspects of Standard Model Physics, non-abelian gauge theories and path integral quantisation. 

These complaints have since been quelled, with recent publication of the 2nd volume (and its associated solutions manual) of this series, covering all the above.

In conclusion, for a beginner graduate student who has never even heard of quantum field theory or researcher wanting a refresher (even a reference), Klauber's work is nothing less than a masterpiece of pedagogical brilliance that will stand the test of time.