Preprint / Version 1

Supersymmetric Theory of Stochastic Dynamics

##article.authors##

  • Sourangshu Ghosh Indian Institute of Science Bangalore

DOI:

https://doi.org/10.31224/6432

Keywords:

Stochastic Dynamics, Supersymmetric Theory, Dynamical systems theory, Topological quantum field theory, Stochastic differential equation, Supersymmetry in dynamical systems, Supersymmetric theory of stochastic dynamics, Topological supersymmetry, Topological field theories, Stochastic dynamical systems, Self-organized criticality, Stochastic chaos, Generalized transfer operator, Chaos Theory, Complex Systems, Nonlinear Dynamics, Statistical Mechanics, Nonequilibrium Physics, Spectral theory of evolution operators, Path integrals, Cohomological/topological methods, Quantum field theory, Supersymmetry, Pseudo-Hermitian operators, Evolution operators of SDEs, Spectral classification of stochastic chaos, Equivariant cohomology, Witten index, Topological invariants, Supersymmetry generator, Exterior derivative, Parisi–Sourlas SUSY interpretation, Differential forms on phase space, Pullbacks induced by stochastic flows, Parisi–Sourlas stochastic supersymmetry

Abstract

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.

Downloads

Download data is not yet available.

Downloads

Posted

2026-02-05

License

Copyright (c) 2026 Sourangshu Ghosh

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.