QUANTUM CHROMODYNAMICS

These lectures provide an overview of Quantum Chromodynamics (QCD), the $SU(3)_C$ gauge theory of the strong interactions. After briefly reviewing the empirical considerations which lead to the introduction of {\it colour}, the QCD Lagrangian is discussed. The running of the strong coupling and the associated property of {\it Asymptotic Freedom} are analyzed. Some selected experimental tests and the present knowledge of $\alpha_s$ are summarized. A short description of the QCD flavour symmetries and the {\it dynamical breaking of chiral symmetry} is also given.Comment: LaTeX, 51 pages, 32 figures (included in separate .uu file) Lectures at the 1994 European School of High-Energy Physics (Sorrento, 1994

Quantum Chromodynamics

After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to perturbative QCD, from tree-level processes to higher-order corrections in renormalized perturbation theory, including jet production in e+ e- annihilation, hadronic tau decays and deep inelastic scattering. The final two lectures treat various aspects of QCD beyond perturbation theory. The main theme is effective field theories, from heavy quarks to the light quark sector where the spontaneously broken chiral symmetry of QCD plays a crucial role.Comment: 48 pages, 28 figures. Lectures given at the 2005 European School of High-Energy Physics, Kitzbuehel, Austria, Aug. 21 - Sept. 3, 2005; to appear in the Proceedings (CERN Yellow Report

Quantum Chromodynamics

Quantum chromodynamics is the quantum gauge field theory that describes the strong interactions. This article reviews the basic structure, successes and challenges of quantum chromodynamics as it manifests itself at short and long distances, including the concepts of asymptotic freedom, confinement and infrared safety.Comment: 23 pages, 3 figures. Contribution to the Elsevier Encyclopedia of Mathematical Physics, in Elsevier forma

Lattice Quantum Chromodynamics

This lecture provides an introduction to quantum chromodynamics (QCD) on the lattice. The continuum limit and Monte Carlo simulations are briefly discussed. Different facets of QCD are nicely exhibited by the potential of a static quark and anti-quark pair and results from lattice calculations of this quantity will be presented.Comment: 17 pages, 5 figures. Proceedings from the Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity", 31 August - 23 September, 2016, Corfu, Greec

Octonion Quantum Chromodynamics

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann \lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann \lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons

Three Dimensional Quantum Chromodynamics

The subject of this talk was the review of our study of three ($2+1$) dimensional Quantum Chromodynamics. In our previous works, we showed the existence of a phase where parity is unbroken and the flavor group $U(2n)$ is broken to a subgroup $U(n)\times U(n)$. We derived the low energy effective action for the theory and showed that it has solitonic excitations with Fermi statistic, to be identified with the three dimensional ``baryon''. Finally, we studied the current algebra for this effective action and we found a co-homologically non trivial generalization of Kac-Moody algebras to three dimensions.Comment: 7 pages, Plain TEX, talk presented by S.G. Rajeev at the XXVI INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS, DALLAS TX AUG. 199

Quantum chromodynamics quark benzene

A six-quark state with the benzene-like structure is proposed and studied based on color string model. The calculation with the quadratic confinement show that such structure has the lowest energy among the various hidden color six-quark structures proposed so far. Its possible effect on $NN$ scattering is discussed.Comment: 5 pages, 7 figure