Field correlators in QCD. Theory and applications

Abstract

This review is aimed to demonstrate the basics and use of formalism of gauge-invariant nonlocal correlators in nonabelian gauge theories. Many phenomenologically interesting nonperturbative aspects of gluodynamics and QCD can be described in terms of correlators of the nonabelian field strength tensors. It is explained how the properties of correlator ensemble encode the structure of QCD vacuum and determine different nonperturbative observables. It is argued that in gluodynamics and QCD the dominant role is played by the lowest nontrivial two-point correlator (Gaussian dominance). Lattice measurements of field correlators are discussed. Important for the formalism theoretical tools, such as nonabelian Stokes theorem, background perturbation theory, cluster expansion, as well as phenomenological applications to the heavy quarkonium dynamics and QCD phase transition are reviewed.Comment: LaTeX, 77 pages, 7 eps-figure

Asymptotic behavior of Wilson loops from Schrödinger equation on the gauge group

“…Such decomposition clarifies the physical meaning of the amplitude ψ(g; γ): as the Wilson loop calculated in k-th representation characterizes interaction of static colour charges in this representation [6,7,8], the function ψ(g; γ) describes simultaneously interaction between colour charges in all representations.…”

“…The properties of Wilson loops are known from lattice simulations and from predictions of different phenomenological models [5,6,7,8].…”

“…Wilson area law means that W k (γ) = exp(−σ k S γ ), where σ k is the tension of QCD string between charges in k-th representation [6,7,8] and S γ is the minimal area of the surface spanned on the loop γ. Wilson area law implies linear interaction potential V (R) = σ k R between static colour charges [5]. If Casimir scaling holds, the tension σ k is proportional to the eigenvalue of quadratic Casimir operator in k-th representation: σ k = σC k , where σ is some constant.…”

“…This formalism allows one to consider the dynamics of Yang-Mills fields as dynamics of chiral fields on loop space and is particularly useful in investigating the relation between gauge theories and string theories [1,4]. Asymptotic behavior of loop variables at large distances is known to be closely connected with the confining properties of the theory [5,6,7,8]. In the conventional picture of confinement colour charges are connected by QCD string, which corresponds to the well-known Wilson area law for the Wilson loop [5].…”

“…In this paper we investigate the probability distribution of parallel transporters on the group manifold and the corresponding amplitude, which is the quantum counterpart of classical loop variables. It is shown that when the Wilson area law [5] and Casimir scaling [7,8] hold for quantum gauge field, this amplitude can be obtained as the solution of the free Schrödinger equation on the group manifold. Solutions of this equation are then expressed in terms of path integral.…”