Heavy Particle Effective Field Theories

Starting from a theory of heavy particles and antiparticles, the path integral formulation of an effective field theory which describes the low momentum interactions is presented. The heavy degrees of freedom are identified and explicitly integrated out from the functional integral of the full theory. Using this method, the effective Lagrangian, which may be calculated to arbitrary subleading order in an inverse mass expansion, is derived for fields of spin-0, 1/2, and 1.