Supersymmetric Theory of Stochastic Dynamics

This monograph develops a fully rigorous mathematical foundation for the supersymmetric structure underlying stochastic dynamics. We present a synthesis of measure theory, differential geometry, and quantum field theory with complete proofs, functional analytic rigor, and geometric intuition. Our goal is to place the Parisi–Sourlas supersymmetry and its generalizations on the same level of precision as stochastic analysis in the sense of Itô, Stroock, and Varadhan.