Renormalization Of Yang Mills Theory In The Light Cone Gauge Using Lagrange Multiplier Field

This volume deals with canonical quantization, Feynman rules and renormalization of Yang-Mills theories in algebraic non-covariant gauges (typically axial and light-cone gauges). The material is self-contained and presented in a basic manner according to a personal style representative of a long lasting activity in the field. Emphasis is always placed on the underlying basic concepts of Quantum Field Theory, even when particular examples are treated, details and the related difficulties are thoroughly discussed. The value of the book goes beyond the specificity of its subject.

This volume is a natural continuation of the book Algebraic Renormalization, Perturbative Renormalization, Symmetries and Anomalies, by O Piguet and S P Sorella, with the aim of applying the algebraic renormalization procedure to gauge field models quantized in nonstandard gauges. The main ingredient of the algebraic renormalization program is the quantum action principle, which allows one to control in a unique manner the breaking of a symmetry induced by a noninvariant subtraction scheme. In particular, the volume studies in-depth the following quantized gauge field models: QED, Yang-Mills theories and topological models (the Chern-Simons and the BF model) in the context of axial-like gauges.

The idea of this book originated from two series of lectures given by us at the Physics Department of the Catholic University of Petr6polis, in Brazil. Its aim is to present an introduction to the "algebraic" method in the perturbative renormalization of relativistic quantum field theory. Although this approach goes back to the pioneering works of Symanzik in the early 1970s and was systematized by Becchi, Rouet and Stora as early as 1972-1974, its full value has not yet been widely appreciated by the practitioners of quantum field theory. Becchi, Rouet and Stora have, however, shown it to be a powerful tool for proving the renormalizability of theories with (broken) symmetries and of gauge theories. We have thus found it pertinent to collect in a self-contained manner the available information on algebraic renormalization, which was previously scattered in many original papers and in a few older review articles. Although we have taken care to adapt the level of this book to that of a po- graduate (Ph. D. ) course, more advanced researchers will also certainly find it useful. The deeper knowledge of renormalization theory we hope readers will acquire should help them to face the difficult problems of quantum field theory. It should also be very helpful to the more phenomenology oriented readers who want to famili- ize themselves with the formalism of renormalization theory, a necessity in view of the sophisticated perturbative calculations currently being done, in particular in the standard model of particle interactions.

The future of physics -- revisited / C.N. Yang -- Quantum chromodynamics - the perfect Yang-Mills gauge field theories / 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 / T.T. Wu & S.L. Wu -- Senario for the renormalization in the 4D Yang-Mills theory / Ludwig 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 -- Generalization of the Yang-Mills theory / George Savvidy -- Some thoughts about Yang-Mills theory / Anthony 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 / Hong Mo Chan -- The framed standard model (II) - a first test against experiment / Sheung Tsun Tsou -- 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 McKellar -- Yang-Mills for historians and philosophers / Robert Crease -- Gauge concepts in theoretical applied physics / Seng Ghee Tan & M.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 Kauffman -- The scattering equations and their off-shell extension / Edward Yao York Peng -- Feynman geometries / Hu Sen & Andrey Losev -- Particle accelerator development: selected examples / Jie Wei -- A new storage-ring light source / Alexander Chao -- New contributions to physics by Prof. Yang: 2009-2011 / Zhong Qi Ma -- "Brief overview of C.N. Yang's 13 important contributions to physics" / Yu Shi.