Invariants from classical field theory

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern–Simons, and two-dimensional Yang–Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss’ and the second Milnor’s invariant for links in S3, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.