Numerical study of quark confinement in low-dimensional Abelian gauge models

Hoping to gain some useful and general insight on the physics of QCD, the author has studied two models which are qualitatively similar to, and much simpler than Quantum Chromodynamics. Using numerical lattice gauge theory techniques, the author has investigated the potential V(L) between two heavy quarks. First, the author has computed the string tension T in compact Quantum Electrodynamics in three dimensions, without light fermions (quarks). As a function of the coupling g, the data shows T to be constrained between the two envelopes in similarity with QCD. Moreover, the author has found the lines of force of this model to behave like a string for G less than or equal to 1.16, i.e., to have an energy density proportional to (1/lnl). In the second part of this work, the author considers Quantum Electrodynamics in two dimensions, this time including the light fermions; the latter are responsible for the screening of the (color) electric field between the heavy quarks, leading to the cut-off c and the screening length L0 above