A modern course in quantum field theory. Volume 1, Fundamentals / Badis Ydri.

"Version: 20190501"--Title page verso.

Includes bibliographical references.

1. Relativistic quantum mechanics -- 1.1. The rotation groups SO(3) and SO(n) -- 1.2. Special relativity -- 1.3. Klein-Gordon equation -- 1.4. Dirac equation -- 1.5. Free solutions of the Dirac equation -- 1.6. Lorentz covariance : first look -- 1.7. Representations of the Lorentz group -- 1.8. Exercises -- 1.9. Solutions

2. Canonical quantization of free fields -- 2.1. Classical mechanics -- 2.2. Classical free field theories -- 2.3. Canonical quantization of a real scalar field -- 2.4. Canonical quantization of free spinor field -- 2.5. Propagators -- 2.6. Discrete symmetries -- 2.7. Poincaré group and Noether's theorem -- 2.8. Exercises -- 2.9. Solutions

3. The phi-four theory -- 3.1. The harmonic oscillator and the S-matrix -- 3.2. Forced scalar field -- 3.3. The phi-four theory -- 3.4. Feynman diagrams for phi-four theory -- 3.5. Exercises

4. The electromagnetic field and Yang-Mills gauge interactions -- 4.1. Covariant formulation of classical electrodynamics -- 4.2. Canonical quantization of the electromagnetic gauge field -- 4.3. Introducing Yang-Mills gauge interactions -- 4.4. Exercises

5. Quantum electrodynamics -- 5.1. Lagrangian density -- 5.2. Wick's theorem -- 5.3. The LSZ reduction formulae and the S-matrix -- 5.4. Some QED processes and QED Feynman rules -- 5.5. Cross-sections -- 5.6. Vertex correction -- 5.7. Electron self-energy -- 5.8. Vacuum polarization -- 5.9. Renormalization of QED -- 5.10. Exercises

6. Path integral quantization of scalar fields -- 6.1. Feynman path integral -- 6.2. Scalar field theory -- 6.3. The effective action -- 6.4. The O(N) model -- 6.5. The 2-loop calculations -- 6.6. Renormalized perturbation theory -- 6.7. Effective potential and dimensional regularization -- 6.8. Spontaneous symmetry breaking -- 6.9. Exercises

7. Path integral quantization of Dirac and vector fields -- 7.1. Free Dirac field -- 7.2. Path integral quantization of gauge vector fields -- 7.3. The beta function and asymptotic freedom -- 7.4. Schwinger-Dyson equations and Ward identities -- 7.5. Chiral symmetry and axial anomaly -- 7.6. Exercises

8. The Callan-Symanzik renormalization group equation -- 8.1. Critical phenomena and the [phi]4 theory -- 8.2. Renormalizability criteria -- 8.3. The Callan-Symanzik renormalization group equation in [phi]4 theory -- 8.4. Renormalization constants and renormalization functions at 2-loop -- 8.5. Critical behavior -- 8.6. Scaling domain (T > Tc ) -- 8.7. Scaling below Tc -- 8.8. Critical exponents at 2-loop and comparison with experiment -- 8.9. Exercises -- Appendices. A. Exercises -- B. Classical mechanics -- C. Classical electrodynamics.

A Modern Course in Quantum Field Theory provides a self-contained pedagogical and constructive presentation of quantum field theory. Here, constructive is not meant in the sense of axiomatic field theory, but it is merely used in the sense that all results must be obtained by an explicit set of calculations from accepted premises by those who start to learn this subject. Written for advanced students the work provides complete material for a two or three semester course, and includes numerous problem exercises, some with detailed solutions.

Postgraduate students in physics.

Also available in print.

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Badis Ydri is currently a Professor of theoretical particle physics, at the Institute of Physics, Annaba University, Algeria. He is also a research associate at the Dublin Institute for Advanced Studies, Dublin, Ireland, and a regular ICTP Associate at the Abdus Salam Center for Theoretical Physics, Trieste, Italy.

Title from PDF title page (viewed on June 5, 2019).