Structure and Equivalence in Classical Field Theories

Sarita Rosenstock (University of California, Irvine)

Sarita Rosenstock, University of California, Irvine

Structure and Equivalence in Classical Field Theories

Scientists and philosophers often invoke parsimony as a theoretical virtue alongside descriptive accuracy, and aim to minimize the amount of structure present in a physical theory as much as possible. But it’s not always clear what it means to reduce structure in a physical theory, or how one would go about doing so. I present a proposal for formalizing structure comparison in physics using category theory, which can be thought of as the mathematical theory of structure. I’ll then show how this method helps elucidate a number of interesting and important issues in the foundations of classical field theories, including general relativity and Yang-Mills theory.