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 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 ?I = 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 ?I = 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 ß 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

Luciano Maiani is emeritus professor of theoretical physics at the University of Rome, “La Sapienza”, and author of more than two hundred scientific publications on the theoretical physics of elementary particles. Together with S. Glashow and J. Iliopoulos, Maiani made the prediction of a new family of particles, those with “charm”, which form an essential part of the unified theory of the weak and electromagnetic forces. He has been president of the Italian Institute for Nuclear Physics (INFN), director-general of CERN in Geneva and president of the Italian National Council for Research (CNR). He has promoted the development of the Virgo Observatory for gravitational wave detection, the neutrino beam from CERN to Gran Sasso and at CERN has directed the crucial phases of the construction of the Large Hadron Collider (LHC). He has taught and worked in numerous foreign institutes. He was head of the theoretical physics department at the University of Rome, “La Sapienza”, from 1976 to 1984 and held the chair of theoretical physics from 1984 to 2011. He is a member of the Italian Lincean Academy and a fellow of the American Physical Society. For his scientific work, he has been awarded the J. J. Sakurai Prize, the Enrico Fermi Prize, the Dirac Medal, the High Energy and Particle Physics Prize of EPS and the Bruno Pontecorvo Prize.

Omar Benhar is an INFN research director and teaches gauge theories at the University of Rome, “La Sapienza”. He has worked extensively in the United States as a visiting professor at the University of Illinois and Old Dominion University, and was an associate scientist at the Thomas Jefferson National Accelerator Facility. Since 2013, he has served as an adjunct professor at the Centre for Neutrino Physics of Virginia Polytechnic Institute and State University. He is the author of more than one hundred scientific papers on the theory of many-particle systems, the structure of compact stars and electroweak interactions of nuclei.

Nicola Cabibbo (1935–2010) was professor of Theoretical Physics and Elementary Particle Physics 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 Universite 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 United States, 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.