Factorization of Time-Ordered Exponentials for Wiener Space Transformations

Abstract

We develop an operator-algebraic framework for change-of-variables formulas on Wiener space, interpreting them as arising from hidden symmetries acting on observables. We show that general transformations can be represented by time-ordered exponentials generated by annihilation and creation operators, and that these admit an explicit factorization into a determinant, a multiplication operator, and a translation operator. Taking expectations recovers the classical formulas, including the Ramer--Kusuoka formula.