216 pages, 9x6 inches
Oct 2002 Hardcover
ISBN 1-58949-024-X
US$48

 
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The only prerequisites for this book are a knowledge of partial differential equations, Maxwell’s theory of electromagnetism, and the material of Volume 1. An introduction is given to the special theory of relativity, to the relativistic reformulation of Maxwell’s equations, and also to unbounded operators on Hilbert space. The basic goal is the setting up of rules for drawing Feynman graphs and for calculating amplitudes from them. This is done primarily in quantum electrodynamics; but an appendix sketches the extension to the electroweak theory, and Feynman rules are given for this extended Lagrangian. Each chapter is complemented by ten problems, and the student is advised to try them all by himself or herself before looking at our solutions in Volume 4.


undergraduate students, graduate students, teachers, researchers interested in modern physics.
 

1.  Relativity and Quantization
Unbounded Operators on Hilbert Space
Rigged Hilbert Spaces and Operator Algebra
Special Theory of Relativity
Schrödinger and Klein-Gordon Equations
Dirac Equation
Dirac's Views
Exercises

2.  Charged Particle in Electromagnetic Field
Maxwell's Equations
Covariant Derivative
Pauli Equation
Spin-Orbit Coupling
Atomic Physics
Exercises

3.  Dirac Hydrogen Atom
Scalar Central Potential
Solution of Dirac Equation
Bound-State Formula
Dirac Spinors
Particle and Spin Projection Operators
Exercises

4.  Quantum Field Theory
Scalar Field
Electromagnetic Field
Spinor Field
Exercises

5.  Group Theory and the Noether Theorem
Rotation Group and SU(2)
Poincaré group and SL(2,C)
Noether Theorem
Parity, Time Reversal and Charge Conjugation
Exercises		 6.  Scattering Theory and Feynman Graphs
Asymptotic Fields
LSZ Reduction
Wick's Theorem
Diagrams in Momentum Space
Exercises

7.  Quantum Electrodynamics
LSZ Formalism for QED
Compton Scattering
Møller Scattering
Photon-photon Scattering
Exercises

8.  Dimensional Regularization
Rationale for the Method Scattering Theory
Fermion Self-Energy
Vacuum Polarization
Cutkosky Rule
Magnetic Moment and g-Factor of Electron
Exercises

9.  Dyson-Schwinger Equations
Vertex Function
Dyson-Schwinger Equations
Ward-Takahashi Identity
Chiral Symmetry Breaking in Strong QED
Exercises

Appendix

Electroweak Interactions
Spontaneous Symmetry Breaking
Leptonic Sector
Quark Sector
Experimental Tests
Exercises


 
David ATKINSON  received his Ph.D., under Hamilton, from Cambridge University in 1964, and has been a professor of theoretical physics at U of Groningen since 1972. He worked as a visiting scientist at CERN, UC Berkeley, Rome University, Bonn University, Imperial College, Tata Inst., University of Canberra, Yukawa Inst, etc. Dr. Atkinson is well known partly for his excellent and solid research works on the strong interaction S-matrix theory, the mathematical and numerical study of phase-shift analysis, the Dyson Schwinger equations, both in QED and QCD, and the quark propagator equations and chiral symmetry breaking. He has published over 100 research papers in the well-known journals. His recent interest is in the problem of interpretation in probability theory and quantum mechanics. Prof. Atkinson has been teaching quantum mechanics and quantum field theory for many years.

Porter Wear JOHNSON received his Ph.D. from Princeton University in 1967. He has been a professor of  physics at the Illinois Institute of Technology (IIT) since 1983. Dr Johnson has been the director of Science and Mathematics Initiative for Learning Enhancement (SMILE) Program at IIT since 1993 and the director of Science and Mathematics through Application of Relevant Technology (SMART) program since 2000. His recent research interests in high energy theoretical physics involve dynamical mass generation in formally massless quantum field theories, including a number of studies of fermion mass generation in three and four dimensions. The interest lies in QED in its own right, as well as in other theories for which the effective coupling strength varies quite slowly with changing momentum scale. Dr Johnson has also studied the problem of Chiral Symmetry Breaking in Quantum Chromodynamics, with the goal of understanding low energy hadron phenomenology in the context of these models.