  The spectrum of a system with multiple channels composed of two hadrons with
nonzero total momentum is determined in a finite cubic volume with periodic
boundary conditions using effective field theory methods. The results presented
are accurate up to exponentially suppressed corrections in the volume due to
the finite range of hadronic interactions. The formalism allows one to
determine the phase shifts and mixing parameters of pipi-KK isosinglet coupled
channels directly from Lattice Quantum Chromodynamics. We show that the
extension to more than two channels is straightforward and present the result
for three channels. From the energy quantization condition, the volume
dependence of electroweak matrix elements of two-hadron processes is extracted.
In the non-relativistic case, we pay close attention to processes that mix the
1S0-3S1 two-nucleon states, e.g. proton-proton fusion (pp -> d+ e^+ + nu_e),
and show how to determine the transition amplitude of such processes directly
from lattice QCD.
