Non-perturbative Studies in Quantum Chromodynamics
  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. 
Dipankar Chakrabarti