An Introduction to Gauge Theories by Cabibbo, Nicola; Maiani, Luciano; Benhar, Omar;

Short description:

Written by world-leading experts in particle physics, this new book from Luciano Maiani and Omar Benhar, with contributions from the late Nicola Cabibbo, is based on Feynman’s path integral formulation of quantum field theory.

Long description:

Written by world-leading experts in particle physics, this new book from Luciano Maiani and Omar Benhar, with contributions from the late Nicola Cabibbo, is based on Feynman’s path integral formulation of quantum field theory. Key elements of gauge theories are described—Feynman diagrams, gauge-fixing, Faddeev-Popov ghosts—as well as renormalisation in Quantum Electrodynamics. Quarks and QCD interactions are introduced. Renormalisation group and high-momentum behaviour of the coupling constants are discussed in both QED and QCD, with asymptotic freedom derived at one-loop. These concepts are related to the Higgs boson mass and models of grand unification. The new edition has been updated throughout, with two new chapters presenting an outline of Lattice QCD field theory and the renormalisation group analysis of the prominent ΔI = 1/2 rule in kaon decay. The most recent Lattice QCD results on the light quark mass spectrum and on a quantitative justification of the  ΔI = 1/2 rule are also discussed. The Chapter on the anomalous magnetic moment of the muon now includes an update on the Lattice QCD determination of the hadronic vacuum polarisation contribution, which turns out to be in good agreement with the most recent experimental determination of the muon g-2.

Key Features:

• Contains renormalisation of QED with examples worked out in full detail alongside original derivations of Ward identities.

• Discusses applications including the calculation of the β functions of QED and QCD and the electro-weak muon anomaly.

• Explores fundamental constants at very high energy to introduce to theories of grand unification, the unnaturalness of scalar fields and the motivations for new physics beyond the Standard Theory.

Table of Contents:

Chapter 1: Introduction. Chapter 2: The Feynman Path Integral. Chapter 3: Towards a Field Theory. Chapter 4: Equations of Motion, Symmetries and Ward's Identity.  Chapter 5: The Electromagnetic Field. Chapter 6: Fermion Fields. Chapter 7: Scattering Processes and the S-Matrix. Chapter 8: Perturbative Green's Functions in λϕ4. Chapter 9: S-Matrix Feynman Diagrams in λϕ4. Chapter 10: Quantum Electrodynamics. Chapter 11: Renormalisation of QED. Chapter 12: Applications of QED. Chapter 13: Renormalisation Group of QED. Chapter 14: Quantising a Non-Abelian Theory. Chapter 15: Unitarity and Ghosts. Chapter 16: The β Function in QCD. Chapter 17: Lattice QCD. Chapter 18: The ΔI = 1/2 Rule in Strange Particles Non-Leptonic Decays. Chapter 19: The Weak Muon Anomaly. Chapter 20: Effective Constants at High Energy and Ideas about Grand Unifications. Chapter 21: Limits on the Mass of the Higgs Boson. Chapter 22: Effective Potential and Naturalness. Appendix A: Transition Amplitude Calculation. Appendix B: Connected Diagrams. Appendix C: Lorentz Invariance and One-Particle States. Appendix D: Reduction Formulae. Appendix E: Integrals. Appendix F: Chiral Symmetry with Wilson Fermions: Basic Formulae. Appendix G: β(λ) and β(gt) Functions. Bibliography. Index.