Abstract

Let $C$ be the open upper light cone in $\mathbb{R}^{1+n}$ with respect to the Lorentz product. The connected linear Lorentz group $ {\rm SO}_\mathbb{R}^0$ acts on $C$ and therefore diagonally on the $N$-fold product $T^N$ where $T = \mathbb{R}^{1+n} + iC \subset \mathbb{C}^{1+n}.$ We prove that the extended future tube ${\rm SO}_\mathbb{C}\cdot T^N$ is a domain of holomorphy