A. Neveu

The Quantum Dual String Wave Functional in Yang-Mills Theories

Abstract From any solution of the classical Yang-Mills equations, we define a string wave functional based on the Wilson loop integral. Its precise definition is given by replacing the string by a finite set of N points, and taking the limit N → ∞. We show that this functional satisfies the Schrodinger equation of the relativistic dual string to leading order in N. We speculate about the relevance of this object to the quantum problem.

The Slope of the Leading Regge Trajectory in Quantum Chromodynamics

Abstract The Wilson loop operator in quantum chromodynamics is interpreted as a string creation operator. A method is developed to study its renormalization properties. From the QCD Heisenberg equations of motion, it is shown to satisfy a functional differential equation which linearizes in a short-range approximation. The hadron spectrum is given by the phonon spectrum of this equation, which is entirely determined by renormalization group arguments. Linear Regge trajectories are obtained, with a slope calculable in terms of the scaling violation in deep inelastic scattering due to asymptotic freedom. A remarkable numerical agreement is observed.

Local harmonicity of the Wilson loop integral in classical Yang-Mills theory

Abstract We extend our recently proposed connection between classical Yang-Mills fields and relativistic strings, to an explicitly Lorentz-invariant formalism, and show that the Wilson loop integral is a locally harmonic functional of the path if the field equations are satisfied. We speculate about the possibility of reconstructing the Yang-Mills field from our functional. In light-cone coordinates, an infinite set of conserved charges is derived.

Hadronic and supersymmetric string states in chromodynamics

Abstract Previous discussions of two of the authors (JLG, AN) are extended to chromodynamics. From Wilson loop integrals, solutions of open-string dynamical equations for infinite slope of Regge trajectories are obtained. In classical chromodynamics, they describe mesons and baryons as open strings which can break in close analogy with dual models. For supersymmetric chromodynamics a supersymmetric extension of the Wilson loop is derived which leads to the dynamics of closed strings with an additional continuous fermionic degree of freedom along the loop.

Non-classical configurations in Euclidean field theory as minima of constrained systems

Abstract We study a systematic method of applying the semiclassical approximation to Euclidean field theory. First, we extract generalized collective coordinates which are not in general zero modes. We then apply the semiclassical approximation to the other degrees of freedom by minimizing the action with constraints. Hence we are using configurations which are not classical solutions of the original system. After Gaussian integration we are left with a truncated system, involving only the collective coordinates, with non-trivial dynamics. In particular, this is a clear-cut way to introduce multi-instanton or meron-type configurations. The collective coordinates should be chosen such that their dynamics are a good approximation to the original system for the physical phenomenon considered; a familiar concept in other branches of physics with many degrees of freedom. The formalism leads naturally to the introduction of dynamics in an extra time evolution; in particular cases, we show that this is a very powerful tool. In this paper, we only discuss general ideas and formalisms. Specific applications are postponed to to later publications.

String dynamics in QCD

Abstract Recent works of the authors on string interpretation of the Wilson loop operators in QCD are reviewed in a self-contained fashion. Although most of the results have already appeared in print, some new materials is presented on renormalization of the Wilson loop operator and on the use of light-cone expansion to derive a linear string-like equation in light-cone formalism.

Dynamic charges in field theories

Abstract The origin of trace coefficients lies in the classical dynamics of perfect or separable systems in one space, one time dimension. However the notion of systems of conserved integrals of the motion carries over to space dimensions of arbitrary degree. Physically, they arise as coefficients in an asymptotic expansion for the partition function for a model gas at high temperature. The integrals are charges in the system that are dynamic and conserved. In some σ models, in one dimension, a non-local dynamic charg e exists which controls the quantum system. The striking similarity between σ models in one space dimension and non-Abelian gauge models suggests they exist there also. In this paper we develop efficient functional techniques for finding dynamic charges in any dimension. One method depends on a path integral representation for the partition function, the other on a contour integral representation for it.

String States in Q.C.D.

It has been conjectured for some time that there exists a correspondence between Yang-Mills fields and a dualresonance model similar to the two-dimensional correspondence between sine-Gordon and Thirring models 1–2. In a recent series of papers 3–6, we have investigated such a possibility more concretely.

Semiclassical Methods in Field Theory

The initial motivation for the introduction of semiclassical methods in field theory comes from facts observed in the dynamics of hadrons. At energies of a few hundred MeV to a few GeV, they behave as though they had a rich extended or composite nature. For example, primitive bound-quark models give a surprisingly good description of static properties. But the notion of potential is incompatible with relativistic kinematics needed at those energies.