  Nonrelativstic effective field theories have shown to be a useful framework
to describe systems of weakly bound particles. This work focuses on the
matching procedure to the underlying relativistic theory. The concept of a
physical mass in the absence of explicit Lorentz symmetry and the matching
conditions for S-matrix elements and Green's functions are discussed in general
for scalar particles. The effective Lagrangians of the pure particle and
anti-particle sectors are constructed explicitely for a Yukawa-type interaction
of a heavy and a light scalar field. Using the proper matching, it is shown
that they reproduce the corresponding relativistic amplitudes in a systematic
expansion in inverse powers of the heavy mass.
