Physics Science

The 3rd edition of that book clarified to a degree the fog left in my mind by a two-semester QFT course. The book is better suited for beginners than Peskin & Shroeder, Mandl & Show or Lahiri & Pal simply because it senses better the difficult points for beginners and tries to explain them at lower level. It focuses on the main concepts and doesn’t try to `cover broad material in shortest time’ or get into extreme computational technicalities totally irrelevant to beginners. The correct historical perspective of many ideas is given and the important historical papers are cited. The theory is frequently compared to the experimental results. Violin string is used as a prototype of a continuous system described by a classical field which is the first field quantized later. The book develops physical intuition showing how a scattering process can be analyzed in full QED (all fields are operators), in semiclassical approximation (all fields are operators except the EM field) or using the lowest level wavefunction approximation (all fields are treated like wave functions just like scattering in nonrelativistic QM) often getting the same result (see chapter 8). Important concepts like Feynman diagrams and Renormalization of a theory are first explored in a simple theoretical playground – a hypothetical `ABC theory’ of three massive scalar fields with an interaction ABC term – and later discussed again in the case of QED with all the complications like fermions and Electromagnetic gauge field.

Topics discussed include gauge invariance principle; relativistic field equations describing free particles like Klein-Gordon and Dirac; Feynman interpretation of the negative energy solutions of Dirac eq. (no its not `antiparticle going back in time’); Dirac equation with EM field; Lagrangian and Hamiltonian densities for continuous systems; quantization of free fields like KG (real and complex scalar), Dirac and Electromagnetic field [the quantization is by postulating commutators/anticommutators, no path integrals]; Normal ordering of operators; Interaction picture for interacting fields, Time ordering of operators, Dyson expansion of the S matrix; Wick’s theorem; scattering processes in QED at tree level; Ward identity; form factors for scattering from non point particle; parton model, Bjorken scaling; diagrams with loops, regularization and renormalization of ultraviolet divergences in QED.

It took me a month and a half to read the book and solve all problems (10 problems per chapter on average). The problems are exactly the ones every beginner should solve and usually revolve about filling in details from the text or proving statements in the text. Solving them is usually easy with a few exceptions and teaches you the typical computational tricks of the trade. You have to know quantum mechanics (at least have seen scattering theory) and special relativity. You have to at least have heard of Green function and contour integration in the complex plane. The book provides nice appendices about all these.

Not everything is crystal clear in that book, sometimes it took me a few days for an idea to sink in or I understood some paragraphs only after I read the whole book. Other ideas I did not understand at all. Sometimes it’s hard to tell what they are trying to say although they say it several times from different angles … The authors should work on expressing an idea in a direct succinct way once and for all instead of repeating several fuzzy versions of it. Overall that book made me understand MUCH more than a regular QFT course and I highly recommend it as a prep for such a course.

Rating: 5 / 5

I received my copy of Aitchison and Hey last week and have nearly finished reading the first volume. So far, the text is living up to its legend: it is very readable, well cited (so the historical context can be reconstructed) and pitched for a graduate student who has seen the topic before but is looking for the kind of “handle” on the subject that is missing in nearly all other volumes on QFT (esp so Peskin). If you are struggling with your first look at QFT, reviewing the subject or trying to get a headstart through self instruction — this book is essential. I would strongly recommend that all physics graduate students read this text after completing the usual third semester grad course in QM that often includes a first look at relativistic QM, KG eqn, and Spinors. I would also recommend that one begin by just READING the book carefully before trying problems. Aitchison and Hey have created a very reader friendly intro to QFT and the standard model that is not watered down.

Take my advice: start reading this book in parallel with your QFT coursework or beforehand if you can. These books are worth every penny and every minute of your study time. Many mysteries are resolved! Enjoy.

Rating: 5 / 5