Wetterich's Equation and its Boundary Conditions for Radon Measures on Locally Convex Spaces

Abstract: Wetterich's equation and corresponding flows of effective average actions are used frequently in theoretical physics to study the properties of quantum field theories. Under appropriate conditions, Wetterich's equation also holds for Radon measures on locally convex spaces and the domain of the effective average action is the Lusin affine kernel of the measure. The resulting flow interpolates between the convex conjugate of the cumulant-generating function of the measure in question and its (generalised) Onsager-Machlup function. The underlying metric of the latter is induced by a family of measurable bilinear functionals that can be understood as bilinear versions of Lusin measurable linear functionals.