A path-integral approach to the Cameron-Martin-Maruyama-Girsanov formula associated to a bi-Laplacian (Q1936450)

Summary: We define the Wiener product on a bosonic Connes space associated to a bi-Laplacian, and we introduce formal Wiener chaos on the path space. We consider the vacuum distribution on the bosonic Connes space and show that it is related to the heat semigroup associated to the bi-Laplacian. We deduce a Cameron-Martin quasi-invariance formula for the heat semigroup associated to the bi-Laplacian using some convenient coherent vector. This paper enters under the Hida-Streit approach of path integral.