World-Line Formalism: Non-Perturbative Applications

Abstract

This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields.

Keywords

• the world-line formalism
• Wilson loops
• analytic calculations of path integrals with the minimal-area surfaces
• theoretical foundations of the stochastic vacuum model
• confinement and chiral-symmetry breaking in QCD
• gluonic bound states
• Casimir scaling
• the Yang-Mills running coupling
• thermodynamics of the gluon plasma
• electroweak phase transition