Interpreting Effective Field Theories

An effective field theory (EFT) is a theory of the dynamics of a physical system at energies small compared to a given cut-off. Low-energy states with respect to this cut-off are effectively independent of states at high energies; hence one may study the low-energy dynamics without the need for a detailed description of the high-energy dynamics. Many authors have suggested that, because of the essential role the cut-off plays in the standard (Wilsonian) method of constructing an EFT, an appropriate interpretation of an EFT requires a realistic interpretation of the cut-off. For some, this suggests an ontology of "quasi-autonomous domains" (Cao and Schweber 1993); for others, it suggests an ontology in which space is discrete and finite (Fraser 2009); and for yet others, it suggests that EFTs engage in idealizations and are inherently approximate (Fraser 2009, Castellani 2002). I argue that these interpretations are not forced upon us, in so far as there is an alternative to the Wilsonian method for constructing an EFT that does not explicitly employ a cut-off.