  We determine the quantization condition for the energy levels of two
interacting particles in a finite box in a ``moving frame'', i.e. one in which
the total momentum of pions is non-zero. This condition is valid up to
corrections which fall exponentially withe the box size, and holds only below
the inelastic threshold. It is derived using field theoretic methods, using a
generalization of previous summation formulae relating sums and integrals over
momenta. The result agrees with that obtained earlier by Rummakainen and
Gottlieb using a relativistic quantum mechanical approach. Technically, we
expand the finite-volume four-point Green function in terms of the
infinite-volume Bethe-Salpeter kernel, and determine the position of the poles.
The final result is written in terms of the two-pion scattering phase shift.
Our result can be used to facilitate the determination of the scattering phase
shift, and can be used to generalize the Lellouch-L\"uscher formula relating
finite-volume two-particle matrix elements to those in infinite volume.
