Nucleon matrix elements of various four-quark operators are evaluated in quenched lattice QCD using Wilson fermions. Some of these operators give rise to twist-four contributions to nucleon structure functions. Furthermore, they bear valuable information about the diquark structure of the nucleon. Mixing with lower-dimensional operators is avoided by considering appropriate representations of the flavour group. We find that for a certain flavour combination of baryon structure functions, twistfour contributions are very small. This suggests that twist-four effects for the nucleon might be much smaller than m 2 p /Q 2 .

We describe the results of a systematic high-statistics Monte-Carlo study of finite-size effects at the phase transition of compact U(1) lattice gauge theory with Wilson action on a hypercubic lattice with periodic boundary conditions. We find unambiguously that the critical exponent ν is lattice-size dependent for volumes ranging from 4 4 to 12 4 . Asymptotic scaling formulas yield values decreasing from ν(L ≥ 4) ≈ 0.33 to ν(L ≥ 9) ≈ 0.29. Our statistics are sufficient to allow the study of different phenomenological scenarios for the corrections to asymptotic scaling. We find evidence that corrections to a first-order transition with ν = 0.25 provide the most accurate description of the data. However the corrections do not follow always the expected first-order pattern of a series expansion in the inverse lattice volume V −1 . Reaching the asymptotic regime will require lattice sizes greater than L = 12. Our conclusions are supported by the study of many cumulants which all yield consistent results after proper interpretation.

Nucleon form factors have been extensively studied both experimentally and theoretically for many years. We report here on new results of a high statistics quenched lattice QCD calculation of vector and axial-vector nucleon form factors at low momentum transfer within the Symanzik improvement programme. The simulations are performed at three κ and three β values allowing first an extrapolation to the chiral limit and then an extrapolation in the lattice spacing to the continuum limit. The computations are all fully non-perturbative. A comparison with experimental results is made.

We present quenched lattice QCD results for the contribution of higher-twist operators to the lowest non-trivial moment of the pion structure function. To be specific, we consider the combination F π + 2 + F π − 2 − 2F π 0 2 which has I = 2 and receives contributions from 4-Fermi operators only. We introduce the basis of lattice operators. The renormalization of the operators is done perturbatively in the MS scheme using the 't Hooft-Veltman prescription for γ 5 , taking particular care of mixing effects. The contribution is found to be of O(f 2 π /Q 2 ), relative to the leading contribution to the moment of F π + 2 .

As an example of an application of lattice QCD we describe a computation of four-quark operators in the nucleon. The results are interpreted in a diquark language.