Problem Book in Quantum Field Theory

1. Front Matter

   Pages I-X

   PDF

2. Problems

   1. Front Matter

      Pages 1-1

      PDF

   2. Lorentz and Poincaré symmetries

      Pages 3-7

   3. The Klein-Gordon equation

      Pages 9-11

   4. The γ-matrices

      Pages 13-16

   5. The Dirac equation

      Pages 17-24

   6. Classical field theory and symmetries

      Pages 25-30

   7. Green functions

      Pages 31-34

   8. Canonical quantization of the scalar field

      Pages 35-41

   9. Canonical quantization of the Dirac field

      Pages 43-47

   10. Canonical quantization of the electromagnetic field

       Pages 49-53

   11. Processes in the lowest order of perturbation theory

       Pages 55-60

   12. Renormalization and regularization

       Pages 61-64

3. Solutions

   1. Front Matter

      Pages 65-65

      PDF

   2. Lorentz and Poincaré symmetries

      Pages 67-76

   3. The Klein-Gordon equation

      Pages 77-84

   4. The γ-matrices

      Pages 85-92

   5. The Dirac equation

      Pages 93-119

   6. Classical fields and symmetries

      Pages 121-129

   7. Green functions

      Pages 131-140

This Problem Book is based on the exercises and lectures which I have given to undergraduate and graduate students of the Faculty of Physics, University of Belgrade over many years. Nowadays, there are a lot of excellent Quantum Field Theory textbooks. Unfortunately, there is a shortage of Problem Books inthis?eld,oneoftheexceptionsbeingtheProblemBookofChengandLi[7]. The overlap between this Problem Book and [7] is very small, since the latter mostly deals with gauge ?eld theory and particle physics. Textbooks usually contain problems without solutions. As in other areas of physics doing more problems in full details improves both understanding and e?ciency. So, I feel that the absence of such a book in Quantum Field Theory is a gap in the literature. This was my main motivation for writing this Problem Book. To students: You cannot start to do problems without previous stu- ing your lecture notes and textbooks. Try to solve problems without using solutions; they should help you to check your results. The level of this Pr- lem Book corresponds to the textbooks of Mandl and Show [15]; Greiner and Reinhardt [11] and Peskin and Schroeder [16]. Each Chapter begins with a short introduction aimed to de?ne notation. The ?rst Chapter is devoted to the Lorentz and Poincar´ esymmetries. Chapters 2, 3 and 4 deal with the re- tivistic quantum mechanics with a special emphasis on the Dirac equation. In Chapter 5 we present problems related to the Euler-Lagrange equations and the Noether theorem.

• Dirac
• Dirac equation
• Field Theory
• Green Function
• Klein Gordon
• Lorentz
• Perturbation Theory
• Poincaré
• Quantization
• Renormalization
• Symmetries

From the reviews:

"There is, as the author of this book points out, a shortage of books of problems on quantum field theory. This one is based on exercises set to undergraduate and graduate students of the University of Belgrade. There are 64 pages of problems and the solutions occupy a further 171 pages. There is a bibliography and an index. … The book would serve well to accompany an introductory course on QFT." (Lewis H. Ryder, Mathematical Reviews, Issue 2007 c)

"The book provides the reader with about 200 problems on different topics in quantum field theory … . The material covered and the level of exposition make the book typically appropriate for graduate and undergraduate students in physics. It is actually one of the first problem books in quantum field theory, and can be very useful students both following a course and studying on their own." (Bassano Vacchini, Zentralblatt MATH, Vol. 1102 (4), 2007)

• Faculty of Physics, University of Belgrade, Belgrade, Serbia and Montenegro

  Voja Radovanovič

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