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A First Book of Quantum Field Theory, by Amitabha Lahiri, Palash B. Pal
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This book introduces QFT for a reader with no prior knowledge of the subject. It is meant to be a textbook for advanced undergraduate or beginning postgraduate students. The book discusses quantization of fields, S-matrix theory, Feynman diagrams, calculation of decay rates and cross sections, renormalization, symmetries and symmetry breaking. Some background material on classical field theory and group theory, needed for the exposition, are also presented in the book. Detailed calculations of weak and electromagnetic processes are included. There are many exercise problems to help the students, instructors and beginning researchers in the field. The second edition improves upon some notations and explanations, and includes answers to selected exercises.
- Sales Rank: #2618711 in Books
- Published on: 2005-11-30
- Original language: English
- Dimensions: 10.00" h x 6.50" w x 1.00" l, 1.70 pounds
- Binding: Hardcover
- 380 pages
About the Author
Amitabha Lahiri.: S.N. Bose Centre for Basic Sciences Palash B. Pal.: Saha Institute of Nuclear Physics
Most helpful customer reviews
38 of 39 people found the following review helpful.
Finally an "easy" book on QFT
By Rehan Dost
I had to specially order this book but it was well worth it.
To start the authors presuppose only the standard undergraduate mathematical background. Readers adept in multi-variable calculus and linear algebra with applications to Special Relativity and introductory quantum mechanics will have no difficulty with the book.
The authors present the IDEAS of QFT and then elaborate adding detail in stages with worked examples.
They first introduce classical field theory and develop both the Langrangian and Hamiltonian concepts culminating in the principle of least action. Variational calculus techniques are employed to develop the standard euler langrange equations. Noether's theorem is introduced which roughly speaking, states that for each symmetry of the Langrangian one has a conserved quantity. For example space translation invariance leads to conservation of linear momentum and time symmetry leads to conservation of energy. Two types of symmetries are distinguished, namely internal and external. Lorentz transformations fall within the later category.
Quantization of the energy mass relation is shown to lead to the Klein-Gordon equation which has issues when intrepreted as a wavefunction equation.
We see how the general solution for the Klein-Gordon equation should be intrepreted as an operator equation ( so called second quantization ). This leads to a meaningful reintrepretation of the solution as a quantum field with spacetime acting as a way to label the operators. That is each spacetime point has an infinite collection of annihilation and creation operators ( 1 for each momentum ). Fock space, ground states and normal ordering issues are dealt with. The commutation relationships are explored.
Complex scalar fields are dealt with next with few changes but new phenomena of antiparticles.
The idea of a propagator is introduced namely the transition probability amplitude of the creation of a particle at a spacetime point and annihilation later. This is done using Green functions and then shown to be the same as the above transition amplitude. The importance of time ordering of operators is introduced.
The dirac equation and solutions and second quantization of this field is discussed as are the propogators. It is shown how the hamiltonian derived from the appropriate langrangian has negative energy issues which can only be dealt with by using anticommutation rules. This in turn implies the pauli exclusion principle. Thus the dirac field is suitable in describing spin 1/2 particles.
Thus far the book has dealt with free fields. Now comes the interesting part..interactions. The S matrix is defined and a perturbation expansion explained. Wick expansion is dealt with and we see how the terms in the wick expansion can be pictorially understood.. a natural segueway to Fenyman diagrams. Fenyman rules are introduced. We thus see how the S matrix elements which allow the calculation of transition probabilites between "input" and "output" states can be broken down using wick expansion to individual processes which can be drawn as Fenyman diagrams which can then be used to calculate the probability amplitudes using fenyman rules. This sounds complex but EACH STEP is explained with plenty of examples.
The authors then deal with quantizing the EM field and show how we run into problems unless...new idea here....we introduce gauge fixing. By now you should know what is coming. The field operators are derived as are the propogators and fenyman diagrams for the photon.
We are now ready for QED ( quantum electrodynamics ). It is shown how the langrangian describing the dirac field has a global symmetry. However, as every physics student knows this is not desired in SR which implies local symmetry ( finite speed of light ). Thus trying to make this langrangian have a local symmetry necessitates the introduction of another field....the EM field! This is another idea....called....gauging the global symmetry. Now the QED is applied to electron-positron and compton scattering.
Next the CPT discrete symmetries are dealt with as is renormalization.
The authors then introduce symmetry breaking. That is although the Langrangian may possess the symmetry the ground state may not. They show how symmetry breaking introduces massless particles called goldstone bosons in the case of global symmetries.. The requisite group theory is nicely introduced here. Local symmetries which undergo symmetry breaking are introduced and it is shown how the massless field disappears and how the gauge field terms acquire mass! This is the so called Higgs mechanism and has implications for electroweak theory.
The authors then tackle non-abelian symmetries ( Yang-Mills theories ) just touching on the need for "ghost" fields ( Fadeev Popov method) and Quantum chromodynamics. Briefly the Langrangian for the quarks is "gauged" which produces 8 gauge fields or gluons. There really is no detail here but the reader is inticed to explore more advanced texts.
Finally, electroweak theory is briefly outlined...again the reader is prepared for more advanced texts.
The mathematically mature student with a background in SR and non-relativistic QM will have no problem completing this book in a few months or less.
I would read this book before starting Peskin and Schroeder.
20 of 20 people found the following review helpful.
Terrific introduction to Quantum Field Theory
By Yang Li
This is the textbook when I was learning QFT. I think this is one of the best books for introducing Quantum Field Theory at a postgraduate level. Starting with the reaon why people need QFT, the idea of second quantizaiton is introduced. Both boson and fermion fields are given in a very clear way, followed by Feynman diagrams, Wick's theorem etc. Decay rates and cross sections are calculated with many worked examples. Finally, the ideas of renormalization, symmetry and symmetry breaking, non-Abelian gauge field are included in its second part. The whole book is written in an easy-to-understand language. The important concepts are emphasized with examples. I feels very comfortable when reading this book. This book is not so deep, so if you want to know more about QFT, you need to read other books.
16 of 16 people found the following review helpful.
Learning QFT? Yes, you need this book.
By Matthew T. Haley
This book is reminiscent of Mandl Shaw, another popular "easy" QFT book, but this one's better overall. Mandle Shaw starts out by throwing the Fourier decomposition of the field at you straight away instead of easing you into the subject, following the seeming physics authoring trend of containing an introduction that's only comprehensible once you've finished the book. (Do physics authors know what conclusions are for?) The Lahiri Pal introduction is very readable though, and technicality ramps up in a reasonable way. Also, the writing style of this book is very concise and entertaining. Some chapters read almost like mysteries, starting with puzzles that await solving--much better that the usual approach of meandering without any strategy the reader is aware of. I really like certain sections of Mandl Shaw, such as the explanation of QED Feynman diagrams in Ch. 7, but all in all Lahiri Pal is a much smoother intro to QFT, not because it's easier or dumbed down, but because it's just plain better. My favorite part is the awesome calculation of the anomalous magnetic moment of the electron in 11.3. Hopefully this excellent book's popularity will increase!
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