An Introduction to Gauge Theories

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 integrals. Key elements of gauge theories are described?Feynman diagrams, gauge-fixing, Faddeev-Popov ghosts?as well as renormalization in Quantum Electrodynamics. Quarks and QCD interactions are introduced. Renormalization group and high momentum behaviour of the coupling constants is discussed in QED and QCD, with asymptotic freedom derived at one-loop. These concepts are related to the Higgs boson and models of grand unification.

"? an excellent introduction to the quantum theory of gauge fields and their applications to particle physics. ? It will be an excellent book for the serious student and a good reference for the professional practitioner. Let me add that, scattered through the pages, we can find occasional traces of Nicola Cabibbo's style."
?John Iliopoulos, CNRS-Ecole Normale Supérieure

" ? The volume ends with an illuminating description of the expectation generated by the recent discovery of the Higgs boson, combined with the lack of evidence for super-symmetric particles in the mass range 0.6-1 TeV."
?Arturo Menchaca-Rocha, FinstP, Professor of Physics, Mexico?s National Autonomous University, Former President of the Mexican Academy of Sciences, Presidential Advisor

"?The reader is masterfully guided through the subtleties of the quantum field theory and elementary particle physics from simple examples in Quantum Mechanics to salient details of modern theory."
?Mikhail Voloshin, Professor of Physics, University of Minnesota

Introduction. The Feynman Path Integral. Towards a Field Theory. Equations of Motion, Symmetries, and Ward's Identity. The Electromagnetic Field. Fermion Fields. Scattering Processes and the S-Matrix. Perturbative Green's Functions in Λϕ4. S-Matrix Feynman Diagrams in Λϕ4. Quantum Electrodynamics. Renormalization of QED. Applications of QED. Renormalization Group of QED. Quantizing a Non-Abelian Theory. The Beta Function in QCD. Unitarity and Ghosts. Effective Constants at High Energy and Ideas about Grand Unification. Limits on the Mass of the Higgs Boson. The Weak Muon Anomaly. 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: Beta Functions. Bibliography.

Nicola Cabibbo (1935-2010) was professor of Theoretical Physics and Elementary Particle Phyiscs at the Rome Universities La Sapienza and Tor Vergata, and held research and teaching positions in prestigious institutions such as Harvard University, the Institute for Advanced Studies, Princeton, CERN, Geneva, University of California at Berkeley and Universit□e Paris VI. In 1962, Cabibbo discovered the phenomenon of quark mixing, described by a new natural constant, the Cabibbo angle, measured with great accuracy in semileptonic weak decays of hadrons. According to a recent analysis, Cabibbo's paper on quark mixing was the most influential article published in the journals of the American Physical Society during 1893-2003. In the 1980s, Cabibbo provided important momentum to the applications of numerical techniques to theoretical physics, notably the gauge theories of strong interactions, promoting and leading the development of the family of APE (Array Processor Experiment) supercomputers. He served as a member of a number of learned societies: Accademia Nazionale dei Lincei and Accademia delle Scienze di Torino, in Italy, National Academy of Science and American Association for Art and Sciences, in the USA, and Accademia Pontificia delle Scienze, which he chaired from 1993. An internationally reputed science manager, Cabibbo was President of Istituto Nazionale di Fisica Nucleare (INFN) and of Ente Nazionale per le Nuove Tecnologie per Energia e Ambiente (ENEA). He was the recipient of the J.J. Sakurai Prize (APS), the Medaglia Matteucci (Accademia Nazionale dei XL), the Dirac Medal, (ICTP Trieste), and the Benjamin Franklin Medal.

Luciano Maiani is emeritus professor of theoretical physics at the University of Rome, "La Sapienza", and author of more than two hundred scientic publications on the theoretical physics of elementary particles. Together with S. Glashow and J. Iliopoulos, Maiani made the prediction of a new family