Non-Abelian higher-derivative Chern-Simons theories

The canonical and path-integral quantization of the non-Abelian higher-derivative Chem-Simons model in three dimensions coupled to a matter field is constructed. The expression of the gauge field propagator in the momentum space for this higher-derivative model is computed. In the framework of the perturbative formalism, the diagrammatic and the Feynman rules are analyzed. Among other results, we conclude that higher-derivative terms added to the Lagrangian improve the ultraviolet behavior, rendering the model less divergent.     

Reggeization in Yang-Mills theories

We calculate the high energy fermion-fermion scattering amplitude in Yang-Mills field theory through sixth order in the coupling constant, and find that the amplitude Reggeizes. Our result is simpler than and qualitatively different from an earlier published calculation.     

Stability in Yang-Mills theories

At a solution of the Yang-Mills equations onS ⁴, or the Yang-Mills-Higgs equation on ?³, the hessian of the action functional defines a natural second order, elliptic operator. The number of negative eigenvalues of this operator is bounded below by a multiple of the relevant topological charge. The proof of this assertion requires a relative index theorem for Dirac-type operators on ? ⁿ ,n≧3.     

Yang-Mills string theories

It is shown that the addition of a “colored” Yang-Mills supermultiplet to the locally supersymmetric spinning string Lagrangian does not yield a viable new string model, even though supersymmetry is preserved. However, a Yang-Mills extension of the Veneziano string that yields the color singlet sector of the Bardakçi-Halpern model is constructed.     

Algebroid Yang-Mills theories

A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently many E-Killing vectors leads to an astonishingly mild deformation of ordinary Yang-Mills theories: Additional fields turn out to carry no propagating modes. Instead, they serve as moduli parameters gluing together in part different Yang-Mills theories. This leads to a symmetry enhancement at critical points of these fields, as is also typical for String effective field theories.     

The Continual Approach in the Yang-Mills Theory in the External Non-Abelian Field

The theory of Yang-Mills field in interaction with matter fields is considered in the presence of external gauge field. A closed expression for the generating functional of the Green functions is obtained, and a detailed analysis of the Green functions of the scalar, spinor, ghost and Yang-Mills fields is performed. The path-integral solution for all these Green functions is obtained, which includes the functional averaging over the classical trajectories in the space of commuting and anticommuting variables, the latter being anociated with the particle spin and isospin. For illustration an arbitrary Abelian-like external field is considered, as well as non-Abelian-like constant external field.     

Diffraction scattering in Yang-Mills theories

The infrared problem in Yang-Mills theories is studied in order to elucidate aspects of high energy behavior. The integro-differential equation of Cornwall and Tiktopoulos is used to investigate quark-quark scattering in the limit λ → 0 (λ being the gluon regulator mass), s → ∞ with t fixed. The solution displays the infrared factors explicitly. When this formula is expanded in power series and the leading log is extracted one recovers the perturbation theory calculations to sixth order.     

Factorization and hence reggeization in Yang-Mills theories

We show how to calculate high-energy gauge meson exchange reactions in general, spontaneously broken Yang-Mills theories. We exploit a class of non-covariant gauges in which the scattering amplitudes take on a factorized form in leading order in ln s. Such factorization can only be consistent with Lorentz invariance if the amplitudes have a power law, or Regge behaviour. We evaluate the trajectory functions by a one-loop calculation and verify that the gauge mesons lie on the trajectories.     

Nontrivial quadratic gauge-fixing in Yang-Mills theories

We study renormalizability of a quadratic gauge-fixing choice involving gauge fields. We show that this can be renormalized simultaneously maintaining the BRS invariance since this respects the underlying global SU(n) invariance. However, this choice, too, induces quartic ghost terms in conformity with our earlier results. Physics Publication No. 81-099     

Self duality in super Yang-Mills theories

The self dual condition in superspace is analysed forN=1,2,4 super Yang-Mills theories. A complete solution of all the constraints in terms of a light cone superfieldJ is presented, where the only equation thatJ satisfies is a SUSY generalization of the Yang equation. By reduction of that equation we obtain various two dimensional SUSY models. We introduce the associated linear problem in terms ofJ, whose integrability condition gives us back the super Yang equation and allows us to obtain the Kac-Moody algebra structure of the theory.     

The pressure in lattice Yang-Mills theories

A simple proof is given that the infinite volume limit for the pressure of a lattice Yang-Mills theory exists and is a continuous function of .     

Effective Lagrangians in classical Yang-Mills theories

The formalism of nonlinear electrodynamics is adapted to the Yang-Mills field theory and it is shown that vacuum polarization effects can be described classically through an effective Lagrangian. As an example, an ad hoc Lagrangian is proposed which leads to a simple solution corresponding to a linear plus Coulomb type potential.     

Yang-Mills theories in space-like axial and planar gauges

The quantization of Yang-Mills theories according to a canonical procedure is studied first in the axial gauge A₃^a ≡ 0. We show that the perturbative S-matrix cannot be expressed in terms of well-defined distributions in a Hilbert space involving only physical states without conflicting with unitarity. We then resort to the space-like planar gauge and show that it is possible to define a perturbative S-matrix at the price of introducing a set of free ghost fields. The S-matrix is unitary in the subspace of the physically acceptable states on which A₃^a vanish.     

Combining infrared and low-temperature asymptotes in Yang-Mills theories

We demonstrate that the powerlike nonperturbative behavior of gluon and ghost propagators in the infrared limit of Yang-Mills theories can provide at finite temperatures T a negative T4 contribution to the pressure and energy density. The existence of a mass gap then implies new relations between the infrared critical exponents of gluon and ghost propagators.     

Instantons and monopoles in Yang-Mills gauge field theories

This is a survey article on instantons and monopoles and is intended for those who have no prior knowledge of Yang-Mills gauge field theories. With minimal amount of physical motivation and mathematical apparatus, the basic field equations and their solutions, wherever known, are presented. Particular emphasis is put on those problems which are as yet unsolved.     

Ghost condensates in Yang-Mills theories in the Landau gauge

Ghost condensates of dimension 2 are analyzed in pure SU(N) Yang-Mills theories by combining the local composite operators technique with the algebraic BRST renormalization.