Elements of the general boundary formulation and the composition of local measurements in quantum field theory

In this talk, I will introduce the main elements and ideas of the general boundary formulation [R. Oeckl. A local and operational framework for the foundations of physics. Advances in Theoretical and Mathematical Physics, 23(2):437–592, 2019. arXiv: 1610.09052.]. This is a formalism inspired by quantum gravity approaches and quantum information theoretic ideas and it generalises quantum field theory in such a way to deal with local measurements in local spacetime regions. It can therefore serve as a framework for reconciling quantum field theory with quantum information theory and describe measurement set-ups more general that the scattering (S-matrix) picture of particle physics. This is known to be non-trivial because the naïve application on quantum fields of mathematical objects representing measurements in the non-relativistic theory can lead to violations of locality and causality. This has been indicated by the Reeh-Schlieder theorem, as well as the more recent analysis by Sorkin [R. D. Sorkin. Impossible measurements on quantum fields. In B. L. Hu and T. A. Jacobson, editors, Directions in General Relativity: Papers in Honor of Dieter Brill, Volume 2, volume 2, page 293, January 1993.]. Here, I will focus on the composition of measurements (and observables) in relativistic quantum field theory and discuss how we deal with this problem in the context of the general boundary formulation.