Quantum Field Theory, Rev.Ed.

Rating:
Summary: The one and only book for the beginner.
Review: Let me put it this way: I consider a serious mistake for any student NOT to use this book as their first book in Quantum Field Theory. This book is the absolute must for any beginner before he or she moves on into the "fancier" books of the field.

It starts smoothly and someone need only have a basic course in quantum mechanics and analytical (Lagrangian) dynamics. The nice thing about the book is that it is SELF CONTAINED. You start from chapter one and you can go along through the end without ever needing to open any other book. Everything is in there. Also it has nice and very helpfull appendices that have gothered all the formulae, conventions and diagrams that you need in order to calculat any electroweak cross section.

In this book you will learn all the story about canonical quantization in a very clear and informative way. I consider a CRIME for a physics student to start learning Quantum Field Theory with the path integral approach. You loose immedately the physical picture and the particle content of the theory because you are confronted right from the start with mathematical structures that you have never seen and handling them correctly takes away the physics content of the subject. Believe me I have been there! With Mandl you will always be close to the quantum of the field ,which is the particle, you will see it right in fron of your eyes beeing created, propagated and then annihilated, and you will have a clear picture of what is really going on (quantum theory permitting of course).

Mandl gives you right from the beginning all the tricks and tools of the trade for calculating Feynman diagrams. After reading and understanding this book I personally guarantee to you that will be able to calculate any first order diagram in the electro-weak theory and a lot of higher order diagrams too. He introduces in a very pleasant way the trace theorems and the tricks in order to calculate cross sections.

His treatment of the electroweak Lagrangian is superb. He really starts from the beginning and slowly builds up writing down the whole Lagrangian, its symmetries and its uses. His treatment of the gauge symmetry is a real beauty. It really opens your mind. I could go on forever writting about this great book and how much it helped me cope with this difficult for beginners field. You will not be lost in difficult mathematics that will take away from you the real physics and on the other hand you dont loose anything. He has exactly the right material for a first rigorous course in Quantum Field Theory. His treatment of renormalization is also great.

I consider Mandl to be one of the most prominent pedagogists in the physics field and I have the utmost respect for him. The reason for this is that I have gained a very strong background in both Quantum Field Theory and Statistical Mechanics just by reading his books.

The serious student of particle physics will eventually have to move on to the path integral approach, renormalization of the electro-weak theory, renormalization group, QCD etc. BUT without having a solid background in the topics included in Mandl's book this effort will be fruitless and frustrating. Take my word for it.

Rating:
Summary: Clear and very simple
Review: This book is an introduction to QFT for beginners. It starts from basic lagrangian and hamiltonian formalism, outlines a basic but selfcontained treatment of the bosonic and fermionic free fields; the focus shifts then to interacting fields and introduces the concept of radiative corrections with several examples; gauge theories are then presented in a simple form and the Standard Model of electroweak interactions is described briefly. Simple exercises in every chapter.

Rating:
Summary: Quick overview of quantum field theory
Review: When this book was first written, the intermediate vector bosons had only recently been (indirectly) observed, giving more weight to the gauge theory of electroweak interactions. The first edition did not treat the electroweak theory at all, but this, the revised edition, does, albeit using a formalism that is now considered to be somewhat antiquated. In particular, the methods of functional integration are not used at all. Canonical methods are used instead in the quantization procedures. The reader interested in a fast overview of quantum field theory could benefit from a perusal of the book. There are no fresh insights on quantum field theory in the book, and so it should really be considered as more of a bread-and-butter overview of the subject, with emphasis on the calculations of cross-sections rather than on a deep understanding of quantum field theory. The latter is very difficult both to explain and to research, and readers will have to look elsewhere to obtain this level of knowledge, or, better yet, figure it out for themselves and propose new approaches to quantum field theory, that not only predicts the results coming from scattering experiments, but also solves the major unsolved problem of quantum field theory: the existence of a bound state.