Abstract: Despite being the most accurate theory up to date, Quantum Field Theory (QFT) remains incomplete in its mathematical foundation. This talk examines the concepts of (non) locality within QFT, particularly focusing on the role of real subspaces of a complex Hilbert space. We will discuss the interplay between these subspaces and Algebraic Quantum Field Theory, and how they contribute to the construction of local nets of von Neumann algebras. In particular, we will highlight how these nets maintain key properties when considering the vacuum state, providing further insight into the underlying structure of quantum fields.
