Quantum chromodynamics

Quantum Chromodynamics (QCD) is a quantum field theory of the strong interaction with non-abelian gauge fields mediating the interactions between quarks. The experimentally observed strong interactions are to be epiphenomena of these fundamental interactions. The experimental successes of QCD form the basis for our present optimism that a theory of the strong force has been found. However, QCD is still very vulnerable to default on both experimental and theoretical grounds. In this article we offer the reader a review of the properties and attempted solutions of QCD. Each section of this review can be read independently of the others. In the introduction we describe the properties of QCD and the hoped for confinement and PCAC phase transitions. This is followed by a section on the renormalization of non-abelian gauge field theories: the functional methods and the path integral, the BPHZ program, the BRS transformation and proof of renormalizability, the Slavnov-Taylor identities and Schwinger-Dyson equations. The renormalization group equations are derived and applied to physical processes. Two dimensional prototypes of QCD, the abelian Schwinger model and 2-D QCD, are reviewed. An extensive review of the perturbative development of QCD is given with emphasis on infrared divergences, exponentiation of leading logarithms, the Cornwall-Tiktopoulos equation and a non-perturbative approach to QCD. A self contained section on topological solitons follows with discussions of homotopy theory, vortices, monopoles and especially instantons, and the periodic vacuum. Recent results, the attempt to study phase transitions in QCD using the dilute gas approximation and Borel resummations in QCD, are examined. Most of the major areas of interest in QCD are covered in this review; the prime exceptions are lattice gauge theories and phenomenological QCD like the parton and potential models.