Whence the Effectiveness of Effective Field Theories?. (3rd August 2018) - Franklin, Alexander
Abstract: Effective quantum field theories (EFTs) are effective insofar as they apply within a prescribed range of length-scales, but within that range they predict and describe with extremely high accuracy and precision. The effectiveness of EFTs is explained by identifying the features—the scaling behaviour of the parameters—that lead to effectiveness. The explanation relies on distinguishing autonomy with respect to changes in microstates (autonomyms ), from autonomy with respect to changes in microlaws (autonomyml ), and relating these, respectively, to renormalizability and naturalness. It is claimed that the effectiveness of EFTs is a consequence of each theory's autonomyms rather than its autonomyml . 1 Introduction 2 Renormalizability 2.1 Explaining renormalizability 3 Naturalness 3.1 An unnatural but renormalizable theory 4 Two Kinds of Autonomy 5 The Effectiveness of Effective Quantum Field Theories 6 Conclusion