Fidelity and Wilson Loop for Quarks in Confinement Region

Connection between the stability of quantum motion in random fields and quark confinement in QCD is investigated. The analogy between the fidelity and the Wilson loop is conjectured, and the fidelity decay rates for different types of quark motion are expressed in terms of the parameters which are commonly used in phenomenological and lattice QCD. PACS numbers: 12.38.Aw; 05.45.Mt The property of quark confinement in QCD is believed to be determined by the presence of chaotic solutions in the spectrum of Yang-Mills equations [1, 2]. In this case it is important to investigate connection between the stability of quark motion in random fields and the property of quark confinement.The stability of quantum motion is usually described in terms of the fidelity, and the confining properties are analyzed using the Wilson loop. The aim of this paper is to demonstrate the similarity between this two quantities in QCD and therefore to reveal the analogy between the stability of quark motion and the quark confinement. One usually uses Wilson’s area law for the Wilson loop as a litmus test for quark confinement. Wilson loop is usually defined as the trace of an averaged multiplicative integral over a closed contour C: U (C) = P exp 