  In this thesis, two nonperturbative techniques, namely, similarity
renormalization group (SRG) approach and light-front transverse lattice (LFTL)
approach are studied in the the context of hadron bound state problem in
light-front QCD. We first investigate the meson bound state problem in (2+1)
dimensional QCD using Bloch effective Hamiltonian which serves as a benchmark
for comparative study of the SRG Hamiltonian. In the SRG scheme we compare
three different choices for the similarity factor. In (2+1) dimensions, in the
lowest order, SRG produces linear confinement along the transverse direction
but only square root confinement along the longitudinal direction and thus
breaks the rotational symmetry. In the LFTL approach, we first investigate the
problem associated with fermion formulation on a LFTL. When the symmetric
lattice derivative is used, the doublers arise due to decoupling of even and
odd sub-lattices. We have discussed Wilson fermion and staggered fermion to
remove the doublers. We propose another way of formulating fermions on LFTL by
using asymmetric lattice derivatives in such a way that the Hermiticity of the
Hamiltonian is preserved. There are no doublers in this method. We also discuss
the symmetry relevant for fermion doubling on LFTL. We also compare these two
methods of fermion formulations in the context of meson bound state problem in
(3+1) dimensional QCD with at most one link approximation.
