Renormalization in non-Abelian gauge theories

The renormalization is performed in a manifestly covariant approach. The simplest form of the Ward identities z₁=z₂=…=z_n=… is fulfilled automatically in every gauge. In the Yang-Mills theory the counter-terms are gauge-invariant and depend on the charge renormalization constant only. In pure gravitation the analysis of all divergences is reduced in the present approach to some special classification of the kth order scalar densities in a Riemannian space.     

Multi-meson exchange in non-Abelian gauge theories

We find a new sum rule for the residue of the J = 0 fixed pole in Compton scattering. The sum rule applies to any target and links the residue to a calculable set of contributions from the resonance region. We discuss proton, neutron, deutron and pion targets and the possibility of discriminating from previous models. The relationship with the parton model is noted and the feasibility of measuring pion photoabsorption cross sections is discussed.     

Magnetic monopoles and non-Abelian gauge theories

We review some properties of magnetic monopoles in non-Abelian gauge theories. Removal of Dirac string singularities and generalizations of the Wu-Yang solution that follow from this procedure are described. A discussion of the possible relevance of monopoles in strong interaction models and their role in quark confinement schemes is given. The magnetic monopole soliton discovered by 't Hooft and Polyakov, the first order formalism developed by Bogomolny, and extensions of these ideas are illustrated.Work supported in part by the U.S. Energy Research and Development Administration under Contract No. EY-76-C-02-2232B^*000.     

Infrared instability of the vacuum state of gauge theories and asymptotic freedom

The radiative corrections to the Yang-Mills massless theory are found to lead to an instability of the vacuum state. This fact is in full compliance with the asymptotic freedom of gauge theories and is due to infrared singularities.     

Composite hadrons in non-Abelian lattice gauge theories

Euclidean non-Abelian gauge theories are quantized on a (finite) lattice using functional integration. From the general from of the 2m-point Schwinger function for the fundamental fermions fields, dynamical consequences for composite meson and fermion fields are investigated. The Okubo-Zweig-Iizuka rule is derived and an analogy to non-relativistic potentials for the quark-antiquark and the 3-quark system is exhibited.     

Construction of non-Abelian gauge theories on noncommutative spaces

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. Received: 13 June 2001 / Published online: 19 July 2001     

Covariant quantization of non-Abelian antisymmetric tensor gauge theories

The non-Abelian Freedman-Townsend gauge tensor model is quantized in large class of covariant gauges using the geometrical reinterpretation of the BRS equations. In addition to the now usual pyramid of gauge and ghost states, a pyramid of auxiliary fields is found in our construction. These fields enforce the consistency of equations of motion and the integrability of the BRS equations.     

Disorder,local order and asymptotic freedom in spin and lattice gauge theories

We examine some aspects of the confinement problem from the point of view of simple molecular field and spin wave concepts applied to lattice gauge theory. Our main endeavour is to discover the reasons for the absence of a deconfining phase transition in 4 dimensions. The essential point we make is that the mechanism responsible for eliminating the transition is deeply related to, not to say implied by, asymptotic freedom, which is the principal characteristic of the system at low temperatures and short wavelenghts. Our analysis is built on the analogy of lattice gauge theories with 2-dimensional spin systems.     

Cancellation of infrared divergences in non-Abelian gauge theories

We investigate the infrared problem for non-Abelian gauge fields. Specifically, we show that the transition rate for fermion-fermion scattering suitably averaged over the colors of the fermions is infrared finite to lowest non-trivial order. The finite radiative correction due to soft bosons is given explicitly.     

VII. Difficulties in fixing the gauge in non-Abelian gauge theories

Some problems arising from the use of the Coulomb gauge in SU(2) Yang-Mills theory are discussed. It is shown that: i) the transversality condition does not fix the gauge uniquely (Gribov ambiguity); ii) there exist physical configurations that cannot be described by a continuous A_μ in the Coulomb gauge.     

Uniformly valid amplitude expansions for non-Abelian gauge theories

The imposition of a particular gauge condition in a non-Abelian gauge theory may lead to large-r nonuniformities in an amplitude expansion when used in the construction of an approximate solution of the field equations of the theory. We show that for both the Yang-Mills theory and general relativity it is always possible to find a class of gauge conditions that do not suffer from this defect and at the same time lead to solvable equations in each order of the approximation employed. We further show how one can construct such gauge conditions by a method similar to Lighthill's method of strained coordinates. An example of such a construction is given for the Yang-Mills theory.