Measurements and state updates in quantum field theory

In recent years, a fully covariant framework was developed by Fewster and Verch to describe measurement processes in quantum field theory (QFT), resolving long-standing causality issues arising from trying to adapt standard non-relativistic rules to QFT. This framework is described in terms of the algebraic formulation of QFT (AQFT), which is a naturally well-suited approach for theories on curved spacetimes. While it is known that, in certain models, the class of non-selective measurements preserves the singularity structure associated with so-called Hadamard quantum states, the effect of selective measurements on these states is not yet fully established. This thesis presents a first approach to complete the picture. Techniques from microlocal analysis, distribution theory, and operator algebras are employed to study how the act of performing a selective measurement on a quantum field alters the singularity structure of its Hadamard states. It is shown that there are multiple ways to set up selective measurements, conditioned on local effects of the quantum Weyl algebra, that preserve the Hadamard condition of the preparation state. Conversely, analytical limits where the Hadamard condition is lost are also identified. Examples carrying relevant physical interpretations are presented alongside the development of these general results. Finally, an explicit model is chosen to carry out perturbative computations to analyze the extent to which a measurement process induces variations in the energy density of a specific QFT.