| This thesis describes two projects studying properties of Quantum Chromodynamics using numerical simulations. In the first part of this thesis, we present nonperturbative renormalization constants of fermionic bilinears on the lattice. We have a quenched data set as well as two and one flavor dynamical simulation data sets. All of them use overlap fermions, which respect chiral symmetry on the lattice. We consider the effects of the exact zero modes of the Dirac operator and find that they are important in calculating the renormalization constants of the scalar and pseudoscalar densities, while they are not relevant for the vector and axial vector currents. The results are given in the RI' and MS schemes and compared to perturbative calculations. The one loop perturbative results for the scalar and pseudoscala,r density are found to be not reliable.; In the second part, we calculate point to point vacuum correlators with baryon currents containing diquarks in the color antitriplet representation. We consider the scalar, pseudoscalar and axial vector diquark channels. In the quenched simulation, the scalar diquark channel shows the most attraction. We also find that the attraction in the scalar channel is mainly from zero modes, especially at small quark masses. In the pseudoscalar diquark channel, the zero modes contribute excess repulsion. In the axial vector channel, zero mode contributions seem to be not important. These results are qualitatively consistent with instanton liquid models. Both the dynamical simulation and the quenched simulation results of the correlators show little difference between topological charge |Q| = 1 and Q = 0 sectors. This indicates that the zero mode effects are mainly from big |Q| sectors. Since high Q configurations are suppressed in full QCD, it seems that diquark effects in light baryons are not so important as in quenched QCD. |
