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Quantum Field Theory [Paperback]

Franz Mandl , Graham Shaw
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

26 Oct 1993
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W?? and Z? bosons had been observed and the experimental investigation of high energy electro–weak interactions was in its infancy. Nowadays, W?? bosons and especially Z? bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen–sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro–weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical interpretation is stressed at every point and its use is illustrated in detailed applications. After studying this book, the reader should be able to calculate any process in lowest order of perturbation theory for both QED and the standard electro–weak theory, and in addition, calculate lowest order radiative corrections in QED using the powerful technique of dimensional regularization. Contents: Preface; 1 Photons and electromagnetic field; 2 Lagrangian field theory; 3 The Klein––Gordon field; 4 The Dirac field; 5 Photons: covariant theory; 6 The S–matrix expansion; 7 Feynman diagrams and rules in QED; 8 QED processes in lowest order; 9 Radiative corrections; 10 Regularization; 11 Weak interactions; 13 Spontaneous symmetry breaking; 14 The standard electro–weak theory; Appendix A The Dirac equation; Appendix B Feynman rules and formulae for perturbation theory; Index.


Product details

  • Paperback: 372 pages
  • Publisher: Wiley-Blackwell; Revised Edition edition (26 Oct 1993)
  • Language: English
  • ISBN-10: 0471941867
  • ISBN-13: 978-0471941866
  • Product Dimensions: 22.8 x 15.2 x 2 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 1,713,386 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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"...designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental analysis." (Zentralblatt MATH, Vol. 972, 2001/22)

From the Back Cover

Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro–weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen–sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro–weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical interpretation is stressed at every point and its use is illustrated in detailed applications. After studying this book, the reader should be able to calculate any process in lowest order of perturbation theory for both QED and the standard electro–weak theory, and in addition, calculate lowest order radiative corrections in QED using the powerful technique of dimensional regularization. Contents: Preface; 1 Photons and electromagnetic field; 2 Lagrangian field theory; 3 The Klein—Gordon field; 4 The Dirac field; 5 Photons: covariant theory; 6 The S–matrix expansion; 7 Feynman diagrams and rules in QED; 8 QED processes in lowest order; 9 Radiative corrections; 10 Regularization; 11 Weak interactions; 13 Spontaneous symmetry breaking; 14 The standard electro–weak theory; Appendix A The Dirac equation; Appendix B Feynman rules and formulae for perturbation theory; Index.

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4 of 4 people found the following review helpful
By Alpha
Format:Paperback|Verified Purchase
Mandl & Shaw have a clear objective in mind: to teach a beginner how to do Feynman diagram calculations within the Standard Model of particle physics. Every word, every paragraph is focused towards that aim. Every QFT concept that you need is included, in its logical place. There are no side-remarks or diversions. You don't get any deep insights, but what you do get is a very sharp, undiluted picture of the essential argument.

While QFT books vary wildly their presentation, Mandl & Shaw always opts for the safest option. Mandl & Shaw cover a conventional choice of topics, in the conventional order, in the conventional way. There is nothing particularly individual or original about Mandl & Shaw - just standard explanations and results, arranged in the most sensible order.

When I learned QFT, my lecturers gave me a tough time by telling me to read Peskin & Schroeder. Mandl & Shaw is Peskin & Schroeder made simple: the complications are removed, the journey is straightened out. If you're new to QFT and your goal is to learn to do calculations in particle physics, it's ideal for you. If you're not a beginner or if your main interests are in condensed matter, it's still good to have this book as a reference, but you do need to read more widely.

*NOTE: at the time of writing, all of the other reviews refer to the first edition of this book, which covers only a limited range of material. My review is about the SECOND edition, which is VASTLY expanded. This second edition DOES cover path integrals, non-abelian gauge theories, spontaneous symmetry breaking and renormalization (both the on-shell scheme and the renormalization group). It contains enough content to do ANY perturbative calculation in any sector of the Standard Model.
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7 of 10 people found the following review helpful
5.0 out of 5 stars A good coursebook on Quantum Field Theory 30 Jan 2001
By A Customer
Format:Paperback
A very good first book for someone having the necessary background in Quantum Theory. Covers the essentials in the subject of Field Theory. Easier to penetrate than Weinbergs recent "field theory bible".
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Amazon.com: 4.0 out of 5 stars  12 reviews
70 of 74 people found the following review helpful
5.0 out of 5 stars The one and only book for the beginner. 30 July 2000
By Felix Matathias - Published on Amazon.com
Format:Paperback
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.
23 of 23 people found the following review helpful
5.0 out of 5 stars A very gentle introduction to quantum field theory 7 April 2000
By A Customer - Published on Amazon.com
Format:Paperback
This is the best book from which to learn quantum field theory for the first time. Its very easy to understand and concise. Unfortunately it only treats canonical quantization (no mention of path integrals) and most of the emphasis is on QED. The treatment of SU(2)xU(1) electro-weak theory is a very good introduction to non-abelian gauge theory. Overall, it as an excellent book but need s to be supplemented by a more advanced book like Peskin & Schroeder
11 of 12 people found the following review helpful
5.0 out of 5 stars Thoughtful introduction to QFT 12 Jan 2008
By Amazon Customer - Published on Amazon.com
Format:Paperback
I just want to contribute my five stars.

I'm not a specialist or active in this field, but I enjoy trying to to keep up with interesting things I was led to in college. Hence perhaps I provide the ideal perspective of the perpetual student...

I have several of the other standard texts, which I have at least perused to understand their level and approach. I find Mandl and Shaw to be the best *introduction*. Here are some reasons I like it:

- It is the best book of the bunch that is both completely deep in what it covers and self-contained (but of course it strictly assumes the implicit prerequisites: core quantum mechanics and everything you are likely to have studied if you studied that).
- It focues on the canonical approach. I'm a rabid Feynman worshipper, but in my opinion the path integral approach is best left to the second pass, because it requires two hurdles: a math one-- path calculus--, and a physics one-- shifting focus to the Lagrangian approach to QM. I find the canonical approach a better continuation of core quantum mechanics, hence a better entry point. So learn to count breadth-first; and then have fun discovering you can count it depth-first too.
- The text has a thoughtful logical order of development: Spin 0, 1/2, 1... I think I see a pattern...

Lastly, it is sprinkled with really physically deep commentary on results. Eg, how to understand spin and statistics; or when they frankly describe high-k regularization (a.k.a. math fudging) as possibly modeling new real physics. This arena is both foundational and cutting-edge-- "unfinished"; I like it that they tell it as it is.
9 of 11 people found the following review helpful
4.0 out of 5 stars Clear and very simple 28 Aug 2001
By A Customer - Published on Amazon.com
Format:Paperback
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.
4 of 4 people found the following review helpful
4.0 out of 5 stars clear, but lacks depth 15 Feb 2008
By S. Dorsher - Published on Amazon.com
Format:Paperback
This book is extremely clearly written and is pleasant to read, which is impressive for a text book. However, sometimes it lacks depth on the material it covers. It would be hard to use this as a reference text book and in the class I am taking, the professor finds it necessary to supplement it with other materials.
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