On the 50th anniversary of YangOCoMills theory, this invaluable volume looks back at the developments and achievements in elementary particle physics that ensued from that beautiful idea. During the last five decades, Yang-Mills theory, which is undeniably the most important cornerstone of theoretical physics, has expanded widely. It has been investigated from many perspectives, and many new and unexpected features have been uncovered from this theory. In recent decades, apart from high energy physics, the theory has been actively applied in other branches of physics, such as statistical physics, condensed matter physics, nonlinear systems, etc. This makes the theory an indispensable topic for all who are involved in physics. An international team of experts, each of whom has left his mark on the developments of this remarkable theory, contribute essays or more detailed technical accounts to this volume. These articles highlight the new discoveries from the respective authorsOCO perspectives. The distinguished contributors are: S Adler, F A Bais, C Becchi, M Creutz, A De Rjula, B S DeWitt, F Englert, L D Faddeev, P Hasenfratz, R Jackiw, A Polyakov, V N Popov, R Stora, P van Baal, P van Nieuwenhuizen, S Weinberg, F Wilczek, E Witten, C N Yang. Included in each article are introductory and explanatory remarks by the editor, G OCOt Hooft, who is himself a major player in the development of Yang-Mills theory."

During the last six decades, Yang–Mills theory has increasingly become the cornerstone of theoretical physics. It is seemingly the only fully consistent relativistic quantum many-body theory in four space-time dimensions. As such it is the underlying theoretical framework for the Standard Model of Particle Physics, which has been shown to be the correct theory at the energies we now can measure. It has been investigated also from many other perspectives, and many new and unexpected features have been uncovered from this theory. In recent decades, apart from high energy physics, the theory has been actively applied in other branches of physics, such as statistical physics, condensed matter physics, nonlinear systems, etc. This makes the theory an indispensable topic for all who are involved in physics. The conference celebrated the exceptional achievements using Yang–Mills theory over the years but also many other truly remarkable contributions to different branches of physics from Prof C N Yang. This volume collects the invaluable talks by Prof C N Yang and the invited speakers reviewing these remarkable contributions and their importance for the future of physics. Contents:The Future of Physics — Revisited (C N Yang)Quantum Chromodynamics — The Perfect Yang–Mills Gauge Field Theory (David Gross)Maximally Supersymmetric Yang–Mills Theory: The Story of N = 4 Yang–Mills Theory (Lars Brink)The Lattice and Quantized Yang–Mills Theory (Michael Creutz)Yang–Mills Theories at High Energy Accelerators (George Sterman)Yang–Mills Theory at 60: Milestones, Landmarks and Interesting Questions (Ling-Lie Chau)Discovery of the First Yang–Mills Gauge Particle — The Gluon (Sau Lan Wu)Yang–Mills Gauge Theory and Higgs Particle (Tai Tsun Wu & Sau Lan Wu)Scenario for the Renormalization in the 4D Yang–Mills Theory (L D Faddeev)Statistical Physics in the Oeuvre of Chen Ning Yang (Michael E Fisher)Quantum Vorticity in Nature (Kerson Huang)Yang–Mills Theory and Fermionic Path Integrals (Kazuo Fujikawa)Yang–Mills Gauge Theory and the Higgs Boson Family (Ngee-Pong Chang)On the Physics of the Minimal Length: The Questions of Gauge Invariance (Lay Nam Chang, Djordje Minic, Ahmed Roman, Chen Sun & Tatsu Takeuchi)Generalization of the Yang–Mills Theory (G Savvidy)Some Thoughts about Yang–Mills Theory (A Zee)Gauging Quantum Groups: Yang–Baxter Joining Yang–Mills (Yong-Shi Wu)The Framed Standard Model (I) — A Physics Case for Framing the Yang–Mills Theory? (Chan Hong-Mo & Tsou Sheung Tsun)The Framed Standard Model (II) — A First Test Against Experiment (Chan Hong-Mo & Tsou Sheung Tsun)On the Study of the Higgs Properties at a Muon Collider (Mario Greco)Aharonov–Bohm Types of Phases in Maxwell and Yang–Mills Field Theories (Bruce H J McKellar)Yang–Mills for Historians and Philosophers (R P Crease)Gauge Concepts in Theoretical Applied Physics (Seng Ghee Tan & Mansoor B A Jalil)Yang–Yang Equilibrium Statistical Mechanics: A Brilliant Method (Xi-Wen Guan & Yang-Yang Chen)Chern–Simons Theory, Vassiliev Invariants, Loop Quantum Gravity and Functional Integration Without Integration (Louis H Kauffman)The Scattering Equations and Their Off-Shell Extension (York-Peng Yao)Feynman Geometries (Sen Hu & Andrey Losev)Particle Accelerator Development: Selected Examples (Jie Wei)A New Storage-Ring Light Source (Alex Chao)New Contributions to Physics by Prof C N Yang: 2009–2011 (Zhong-Qi Ma)Brief Overview of C N Yang's 13 Important Contributions to Physics (Yu Shi) Readership: Graduate students and scientists working in high energy physics, statistical physics and condensed matter physics.

Frank Wilczek is one of the foremost theoretical physicists of the past half-century. He has made several fundamental contributions that shape our understanding of high energy physics, cosmology, condensed matter physics, and statistical physics. In all these fields his many discoveries continue to play a key role in shaping the direction of modern theoretical physics.Among Wilczek's major achievements is the discovery of asymptotic freedom, which predicts and explains the ultraviolet behavior of non-abelian gauge theories. The axion, which he co-discovered and named, has emerged as the prevalent candidate for explaining the origin of dark matter in the Universe. His invention of color-flavor locking explains chiral symmetry breaking in high density quantum chromodynamics. His introduction of fractional statistics and anyons are pivotal to our understanding of the fractional quantum Hall effect and form the building blocks of topological quantum computing. His invention of the time crystal concept has catalyzed extensive investigations of dynamical phases of physical systems.Frank Wilczek received the 2004 Nobel Prize in Physics for the discovery of asymptotic freedom. He is also the recipient of several Prizes and honorary awards including the MacArthur Fellowship, the Lorentz Medal of the Royal Netherlands Academy of Arts and Sciences, the Lilienfeld Prize of the American Physical Society, the High Energy and Particle Physics Prize of the European Physical Society, and the King Faisal International Prize for Science of the King Faisal Foundation. He is a member of the National Academy of Sciences, American Academy of Arts and Sciences, and the American Philosophical Society. He is also a foreign member of the Royal Netherlands Academy of Arts and Sciences and of the Royal Academy of Sciences in Sweden.He is currently the Herman Feshbach Professor of Physics at MIT Center for Theoretical Physics. He also holds a professorship at Stockholm University, is a Distinguished Professor at Arizona State University, and is the founding director of the Tsung-Dao Lee Institute and Chief Scientist of the Wilczek Quantum Center at Shanghai Jiao Tong University.This volume serves as a tribute to Frank Wilczek's legendary scientific contributions, commemorating his 70th birthday and the first 50 years of his career as a theoretical physicist. The contributors include several of his PhD students, close collaborators, and both past and present colleagues.

This latest edition enhances the material of the first edition with a derivation of the value of the action for each of the Harrington–Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state. Also included are discussions of the caloron center versus its periphery, the role of the thermal ground state in U(1) wave propagation, photonic particle–wave duality, and calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang–Mills theory. Moreover, a derivation of the temperature–redshift relation of the CMB in deconfining SU(2) Yang–Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed. Contents: Theory:The Classical Yang–Mills ActionThe Perturbative Approach at Zero TemperatureAspects of Finite-Temperature Field TheorySelfdual Field ConfigurationsThe Deconfining PhaseThe Preconfining PhaseThe Confining PhaseApplications:The Approach of Thermal Lattice Gauge TheoryBlack-Body AnomalyAstrophysical and Cosmological Implications of SU(2)CMB Readership: Advanced students, postdocs and researchers in theoretical physics and mathematics, as well as experimentalists.

As part of the commemorative book series on Singapore's 50 years of nation-building, this important compendium traces the history and development of the various sectors of Singapore science in the last 50 years or so. The book covers the government agencies responsible for science funding and research policy, the academic institutions and departments who have been in the forefront of the development of the nation's scientific manpower and research, the research centres and institutes which have been breaking new ground in both basic and applied science research, science museums and education, and the academic and professional institutions which the scientific community has set up to enable Singapore scientists to serve the nation more effectively. Each article is chronicled by eminent authors who have played important roles and made significant contributions in shaping today's achievement of science in Singapore. Professionals, academics, students and the general public will find this volume a useful reference material and an inspirational easy read.

During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956) the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge invariance. In the second stage (1960-1975) it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions. In this work, Lochlainn O'Raifeartaigh describes the former phase. O'Raifeartaigh first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing here for the first time in English, notably by Weyl, Schrodinger, Klein, and London in the pre-war years, and by Pauli, Shaw, Yang-Mills, and Utiyama after the war. The articles illustrate that the reassessment of gauge-theory, due in a large measure to Weyl, constituted a major philosophical as well as technical advance.

During the period 1964OCo1972, Stephen L Adler wrote seminal papers on high energy neutrino processes, current algebras, soft pion theorems, sum rules, and perturbation theory anomalies that helped lay the foundations for our current standard model of elementary particle physics. These papers are reprinted here together with detailed historical commentaries describing how they evolved, their relation to other work in the field, and their connection to recent literature. Later important work by Dr Adler on a wide range of topics in fundamental theory, phenomenology, and numerical methods, and their related historical background, is also covered in the commentaries and reprints. This book will be a valuable resource for graduate students and researchers in the fields in which Dr Adler has worked, and for historians of science studying physics in the final third of the twentieth century, a period in which an enduring synthesis was achieved. Contents: Early Years, and Condensed Matter Physics; High Energy Neutrino Reactions, PCAC Relations, and Sum Rules; Anomalies: Chiral Anomalies and Their Nonrenormalization, Perturbative Corrections to Scaling, and Trace Anomalies to All Orders; Quantum Electrodynamics; Particle Phenomenology and Neutral Currents; Gravitation; Non-Abelian Monopoles, Confinement Models, and Chiral Symmetry Breaking; Overrelaxation for Monte Carlo and Other Algorithms; Quaternionic Quantum Mechanics, Trace Dynamics, and Emergent Quantum Theory; Where Next?. Readership: Graduate students and researchers in theoretical physics; historians and philosophers of science."