R. Jengo

Summing pomeron trees

It is argued that multi-pomeron exchange diagrams not involving pomeron loops play a dominant role in the presently accessible energy range. These diagrams are explicitly summed for a pomeron pole with intercept larger than one (in the limit α′ = 0). s-channel unitarity is automatically satisfied (but not saturated). For particle-particle scattering we obtain phenomenological features in agreement with the data (σT, σel, (d log σeldt)∣t=0 increase to a finite limit and σelσT can be made arbitrarily small). Our results are also applied to nucleus-nucleus scattering.

One-dimensional quantum theory of the pomeron

Abstract The scattering amplitude, originated by the sum over all multi-pomeron exchanges, is evaluated in the zero-slope limit by solving a one-dimensional quantum field theory. In the classical limit, the theory gives back the tree-diagram results obtained in a preceding paper. The constant cross sections obtained in that case for a pomeron with intercept larger than one, are modified only at ultra-asymptotic energies by quantum effects. In the one-dimensional theory, this modification gives rise to cross sections behaving as s − ΔE where ΔE is a small quantity generated by a tunnel effect.

Zero-slope limit of the pomeron field theory

Abstract A reggeon field theory for the pomeron is considered in which the pomeron slope α ′ = 0, following two previous papers on the subject. The resulting one-dimensional theory is put in the form of a Schrodinger equation. Here, the particular ordering of non-commuting operators in the Hamiltonian is considered which properly reproduces the original pomeron field theory. The solution is deduced, together with the precise statement of the symmetry property of the problem and of the relation of our approach with the formal perturbative expansion.

Classical solutions for a generally covariant CP2 non-linear σ-model

Abstract We consider the C P 2 non-linear σ-model in a four-dimensional Riemannian space as a natural extension of the C P 1 non-linear σ-model in two-dimensional flat space. We find two classical solutions, one of the instanton type, with finite action and integer topological charges, and another of the meron type, with infinite action and δ-like topological densities.

Renormalization group analysis of the theory of interacting pomerons

Abstract A detailed analysis of the behaviour near J = 1 and k ⊥ = 0 of the theory of interacting pomerons is performed by means of the renormalization group techniques in the version developed by Wilson. Those techniques deal with the bare field theoretical Langrangian and allow one to study very general forms of the interactions. Following those procedures the strong coupling solution and two different forms of the weak coupling solution are found. The relevance of those solutions for the behaviour of diffractive scattering is briefly discussed.

On the confinement properties of the CPn−1 models in more than two dimensions

We discuss the confinement properties of the CPn−1 models in more than 2 dimensions by three different approaches: by putting them on the lattice, by the 1n expansion in 2 + e dimensions and by semiclassical arguments based on the vortex configurations of the models. Whereas in the 1n expansion the string-like picture of confinement holding in two dimensions turns out to be broken, we find that, both in the lattice and in the semiclassical approach a degenerate case of absolute confinement takes place, as suggested by the equivalence between CP1 and the O(3) σ-model. It is possible to isolate the configurations which determine the degeneracy and to recognize besides them the pattern of a gauge theory with two phases, a Higgs-like and a confining one, respectively.

On the quantum field theory of charges and monopoles

Abstract A treatment of the interaction between charges and monopoles is presented in terms of functional integration over closed paths. The Lorentz covariance is preserved in all the steps of the procedure and the symmetry between electric charges and magnetic poles in the interaction is clearly displayed. Some instances of application are discussed.

Finite temperature approach to confinement

Abstract The finite temperature treatment of gauge theories, formulated in terms of a gauge-invariant variable as in a Polyakov method, is used as a device for obtaining an effective theory where the confinement test takes the form of a correlation function. The formalism isdiscussed for the abelian CP n−1 model in various dimensionalities and for the pure Yang-Mills theory in the limit of zero temperature. In the latter case a class of vortex like configurations of the effective theory which induce confinement corresponds, in particular, to the instanton solutions.

A four-dimensional non-linear σ-model

Abstract We study a four-dimensional version of the non-linear O( n ) σ -model in Euclidean space, introducing a suitable kinetic term in order to have a theory with many of the properties of the two-dimensional model. The outcoming theory is shown to be ultraviolet free for n > 2. Its behaviour is then discussed in the large- n expansion. It is found that in general two phases exist, in one symmetry is broken, in the other preserved, and both are possible in four dimensions. For a range of values of the coupling constant both asymptotic freedom and the perturbative expansion are valid, contrary to the situation of the two-dimensional σ-model. The infrared behaviour is found to be regular and a singularity of the running coupling constant to be of no relevance for the Green functions.

On the instanton effect in the finite temperature Yang-Mills theory and in the non-linear σ-model

Abstract We have considered the effect of instantons at finite temperature on the interquark force and the order parameter of the Yang-Mills theory, finding a sharp change of regime at a temperature close to the one obtained in the Monte Carlo study. We have also considered the problem of the generation of the mass gap in the non linear σ-model in 2 dimensions. This illustrates the role of the instantons, the intrinsic limitations of the approximations made and suggests a physical picture as in the case of Yang-Mills theory.