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

Format:

Book

Author/Creator:

Ydri, Badis, author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP Ebooks Series

Language:

English

Subjects (All):

Quantum field theory--Textbooks.

Quantum field theory.

Genre:

Textbooks

Physical Description:

1 online resource

Edition:

Second edition

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) IOP Publishing [2025]

Biography/History:

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

Summary:

This book provides a self-contained pedagogical and constructive presentation of quantum field theory. It contains a comprehensive introduction to the fundamental topics of quantum field theory starting from free fields and their quantization, renormalizable interactions, critical phenomena, the standard model of elementary particle physics, lattice field theory, the functional renormalization group equation, non-commutative field theory, topological field configurations, exact solutions of quantum field theory, supersymmetry and the AdS/CFT correspondence. Written for advanced students, the work provides complete material for a two or three semester course and includes numerous exercises, some with detailed solutions. Readers of this text will be well prepared to follow the theoretical developments in the field and undertake research projects as part of an MSc or PhD programme

Contents:

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. Initiation to particle physics

2.1. Leptons

2.2. Quarks (hadrons)

2.3. Forces

3. Canonical quantization of free fields

3.1. Classical mechanics

3.2. Classical free field theories

3.3. Canonical quantization of a real scalar field

3.4. Canonical quantization of free spinor field

3.5. Propagators

3.6. Discrete symmetries

3.7. Poincare group and Noethers' theorem

3.8. Exercises

3.9. Solutions

4. The phi-four theory

4.1. The harmonic oscillator and the S-matrix

4.2. Forced scalar field

4.3. The phi-four theory

4.4. Feynman diagrams for phi-four theory

4.5. Exercises

5. The electromagnetic field and Yang-Mills gauge interactions

5.1. Covariant formulation of classical electrodynamics

5.2. Canonical quantization of the electromagnetic gauge field

5.3. Introducing Yang-Mills gauge interactions

5.4. Exercises

6. Quantum electrodynamics

6.1. Lagrangian density

6.2. Wick's theorem

6.3. The LSZ reduction formulas and the S-matrix

6.4. Some QED processes and QED Feynman rules

6.5. Cross sections

6.6. Vertex correction

6.7. Electron self-energy

6.8. Vacuum polarization

6.9. Renormalization of QED

6.10. Exercises

7. Path integral quantization of scalar fields

7.1. Feynman path integral

7.2. Scalar field theory

7.3. The effective action

7.4. The O(N) model

7.5. The two-loop calculations

7.6. Renormalized perturbation theory

7.7. Effective potential and dimensional regularization

7.8. Spontaneous symmetry breaking

7.9. Exercises

8. Path integral quantization of Dirac and vector fields

8.1. Free Dirac field

8.2. Path integral quantization of gauge vector fields

8.3. The beta function and asymptotic freedom

8.4. Schwinger-Dyson equations and Ward identities

8.5. Chiral symmetry and axial anomaly

8.6. Exercises

9. Standard model

9.1. Elements of phenomenology

9.2. The standard model

9.3. Exercises

10. Introduction to lattice field theory

10.1. The lattice 0 4 2

10.2. Fermions on the lattice

10.3. Gauge fields on the lattice

10.4. Quenched quantum electrodynamics on the lattice

11. The Callan-Symanzik renormalization group equation

11.1. Critical phenomena and the f4 theory

11.2. Renormalizability criteria

11.3. The Callan-Symanzik renormalization group equation in f4 theory

11.4. Renormalization constants and renormalization functions at two-loop

11.5. Critical behavior

11.6. Scaling domain (T T > c)

11.7. Scaling below Tc

11.8. Critical exponents at 2-loop and comparison with experiment

11.9. Exercises

Appendix A. Problems

Appendix B. Classical mechanics

Appendix C. Classical electrodynamics

Notes:

"Version: 20250401"--Title page verso

Includes bibliographical references

Online resource; title from PDF title page (viewed on May 1, 2025)

Other Format:

Print version A modern course in quantum field theory

ISBN:

9780750358293

9780750358286

OCLC:

1518431174

Access Restriction:

Restricted for use by site license