  Volume modifications to the binding of two-body systems in large cubic
volumes of extent L depend upon the total momentum and exponentially upon the
ratio of L to the size of the boosted system. Recent work by Bour et al
determined the momentum dependence of the leading volume modifications to
nonrelativistic systems with periodic boundary conditions imposed on the
single-particle wavefunctions, enabling them to numerically determine the
scattering of such bound states using a low-energy effective field theory and
Luscher's finite-volume method. The calculation of bound nuclear systems
directly from QCD using Lattice QCD has begun, and it is important to reduce
the systematic uncertainty introduced into such calculations by the finite
spatial extent of the gauge-field configurations. We extend the work of Bour et
al from nonrelativistic quantum mechanics to quantum field theory by
generalizing the work of Luscher and of Gottlieb and Rummukainen to boosted
two-body bound states. The volume modifications to binding energies can be
exponentially reduced from ~ e^{-kappa L}/L to ~ e^{-2 kappa L}/L in
nonrelativistic systems (where kappa is the binding momentum of the state) by
forming particular combinations of the binding energies determined in the four
lowest-lying boosted systems. Relativistic corrections to this combination, and
others, that violate the exponential reduction are determined. An analysis of
what can be expected from Lattice QCD calculations of the deuteron is
performed, the results of which are representative of a generic loosely bound
system.
