Lattice quantum chromodynamics (QCD) will soon become the primary theoretical
tool in rigorous studies of single- and multi-hadron sectors of QCD. It is
truly ab initio meaning that its only parameters are those of standard model.
The result of a lattice QCD calculation corresponds to that of nature only in
the limit when the volume of spacetime is taken to infinity and the spacing
between discretized points on the lattice is taken to zero. A better
understanding of these discretization and volume effects not only provides the
connection to the infinite-volume continuum observables, but also leads to
optimized calculations that can be performed with available computational
resources. This thesis includes various formal developments in this direction,
along with proposals for improvements, to be applied to the upcoming lattice
QCD studies of nuclear and hadronic systems. Among these developments are i) an
analytical investigation of the recovery of rotational symmetry with the use of
suitably-formed smeared operators toward the continuum limit, ii) an extension
of the Luscher finite-volume method to two-nucleon systems with arbitrary
angular momentum, spin, parity and center of mass momentum, iii) the
application of such formalism in extracting the scattering parameters of the
3S1-3D1 coupled channels, iv) an investigation of twisted boundary conditions
in the single- and two-hadron sectors, with proposals for improving the
volume-dependence of the deuteron binding energy upon proper choices of
boundary conditions, and v) exploring the volume dependence of the masses of
hadrons and light-nuclei due to quantum electrodynamic interactions, including
the effects arising from particles' compositeness. The required background as
well as a brief status report of the field pertinent to the discussions in this
thesis are presented.Comment: Ph.D. thesis, 270 pages, 63 figure
