Gauge-invariant equal-time correlation functions are calculated in lattice QCD within the quenched approximation and with two dynamical quark species. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the ⌬.

We evaluate the isovector nucleon electromagnetic form factors in quenched and unquenched QCD on the lattice using Wilson fermions. In the quenched theory we use a lattice of spatial size 3 fm at β = 6.0 enabling us to reach low momentum transfers and a lowest pion mass of about 400 MeV. In the unquenched theory we use two degenerate flavors of dynamical Wilson fermions on a lattice of spatial size 1.9 fm at β = 5.6 and lowest pion mass of about 380 MeV enabling comparison with the results obtained in the quenched theory. We find that unquenching effects are small for the pion masses considered in this work. We compare our lattice results to the isovector part of the experimentally measured form factors.

We evaluate the nucleon axial form factor, GA(q 2 ), and induced pseudoscalar form factor, Gp(q 2 ), as well as the pion-nucleon form factor, GπNN (q 2 ), in lattice QCD. We also evaluate the corresponding nucleon to ∆ transition form factors, C A 5 (q 2 ) and C A 6 (q 2 ), and the pion-nucleon-∆ form factor GπN∆(q 2 ). The nucleon form factors are evaluated in the quenched theory and with two degenerate flavors of dynamical Wilson fermions. The nucleon to ∆ form factors, besides Wilson fermions, are evaluated using domain wall valence fermions with staggered sea quark configurations for pion masses as low as about 350 MeV. Using these form factors, together with an evaluation of the renormalized quark mass, we investigate the validity of the diagonal and non-diagonal GoldbergerTreiman relations. The ratios GπN∆(q 2 )/GπNN (q 2 ) and 2CA 5 (q 2 )/GA(q 2 ) are constant as a function of the momentum transfer squared and show almost no dependence on the quark mass. We confirm equality of these two ratios consistent with the Goldberger-Treiman relations extracting a mean value of 1.61(2).

We evaluate the N to Delta axial transition form factors in lattice QCD with no dynamical sea quarks, with two degenerate flavors of dynamical Wilson quarks, and using domain wall valence fermions with three flavors of staggered sea quarks. We predict the ratio C(5)(A)(q(2))/C(3)(V)(q(2)) relevant for parity violating asymmetry experiments and verify the off-diagonal Goldberger-Treiman relation.