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Matching in Nonrelativistic Effective Quantum Field Theories

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.