A numerical study of quantum forces. Casimir effect, vortices and Coulomb gauge Yang-Mills theory

In the first part, we present a new numerical approach to the study of physical systems under the influence of external classical fields. Our first investigation concerns the study of magnetic vortex systems, in particular the quantum energy induced by fluctuating fermionic fields. This investigation is relevant for the physics of Type-II superconductors, as well as for the vortex picture of quark confinement in QCD. In a second step, we focus on the study of the Casimir effect. A study of the sphere-plate and cylinder-plate configurations permits to investigate the effects induced by a curved geometry. The second part is devoted to the lattice study of the SU(2) Yang-Mills theory in the Coulomb gauge formulation. The Coulomb gauge gained in recent years increasing interest in relation to the problem of confinement in QCD, since this formulation allows a direct access to the Coulomb interaction potential between static colour sources. We review the properties of the Coulomb gauge approach, in particular the scenario of colour confinement originally formulated by Gribov, and present the results of our lattice simulations for the Coulomb potential, the ghost and gluon propagator. Our numerical estimates are compatible with a linear confinement of static quarks