Discretization methods and analytic bounds for operators in quantum field theory

In this talk, I summarize some of my previous research projects, focusing mostly on two topics.

The first topic is on causal sets, which are the central objects in an approach to quantum gravity, but also serve as a discretization method for quantum field theory (QFT). I review the Poisson process to generate causal sets from spacetime manifolds, and consider quantum fields on such discrete structures.

In the second part, I talk about modular theory in QFT. I explain a (different) numerical discretization scheme that we established to approximate modular Hamiltonians, which are related to information-theoretic measures like relative entropy. During my most recent project, we also formulated analytic bounds for such operators and entropy measures.