Frame dependence of the nonrelativistic limit of quantum fields

We study the nonrelativistic limit of quantum fields for an inertial and a noninertial observer. We show that nonrelativistic particle states appear as a superposition of relativistic and nonrelativistic particles in different frames. Hence, the nonrelativistic limit is frame dependent. We detail this result when the noninertial observer has uniform constant acceleration. Only for low accelerations, the accelerated observer agrees with the inertial frame about the nonrelativistic nature of particles locally. In such a quasi-inertial regime, both observers agree about the number of particles describing quantum field states. The same does not occur when the acceleration is arbitrarily large (e.g., the Unruh effect). We furthermore prove that wave functions of particles in the inertial and the quasi-inertial frame are identical up to the coordinate transformation relating the two frames.