Free fields associated with the relativistic operator - (m - (m~2-Δ)~(1/2))

摘要

The purpose of this article is to consider the construction of free fields associated with the relativistic operator - (m - (m~2-Δ)~(1/2)). The study is based on the viewpoint of pseudo-differential operators, and we present both the Gaussian case and the non-Gaussian infinitely divisible case. We prove that, in the Gaussian case our constructed field is singular with respect to the Gaussian free field based on the non-relativistic m~2 - Δ (Sheffield in Probab Theory Rel Fields 139:512-534, 2007).