Title: From classical to quantum fields on causal sets

Abstract: In this talk, I will give a brief review of algebraic classical and quantum field theory on causal sets. There are different approaches to quantise the classical fields, of which we consider deformation quantisation and geometric quantisation over the symplectic space of the classical field data that is equipped with an inner product. For a free scalar field on a causal set, I show how to define a state associated to the corresponding quantisation map that turns out to be the Sorkin-Johnston state. The geometric construction suggests a natural generalization to less linear examples, such as interacting fields, which is subject to an ongoing project. The main results are based on my PhD project with Eli Hawkins and Kasia Rejzner (arXiv:2207.05667

Talk – Slides

Talk – Video