This article presents a formalized field theory of international migration. Departing from theories of Kurt Lewin, it assumes that the valences of different migration-targets create a field of attracting forces, which may trigger long-range "locomotions". Moreover, the selection among the different possible migration-targets is hypothesized to depend also on an other field of perceived opportunities: the higher the number of vacant holes at a target and the stronger the reporting about these holes by earlier migrants, the stronger the field of perceived opportunities. A mathematical model based on these theoretical assumptions is tested with data about the migration from Poland to other EU-countries. The fit of the model is considerably high and seems to corroborate its field theoretic foundations. The model is further explored by simulating its behavior for different scenarios of valences and perceived opportunities. The article finishes with a summary from the perspective of analytical sociology.