Titel: "An analog of the Beurling-Lax theorem and Quantum Field Theory" Abstract: The classical Beurling-Lax theorem characterizes the Hilbert subspaces of $H^2$ of the upper complex plane that are invariant under positive translations in terms of inner functions. I will describe an abstract real analog of this theorem by means of real subspaces and representations of $SL(2,\mathbb R)$. I will discuss how, by this result, one can build up new families of boundary Quantum Field Theory nets of von Neumann algebras. (Joint work with E. Witten.)