Algebraic construction of interacting QFT models on causal sets

In this talk I will report on recent progress in building QFT models on causal sets. The framework I'm using is that of perturbative algebraic quantum field theory (pAQFT). It was developed for rigorous study of perturbative QFT in the continuum, but can also be applied in the situation where spacetime is replaced by a discrete structure. Causality plays a key role in pAQFT, so it is natural to apply it to causets. Construction of models in this framework is purely algebraic and one does not need to specify a state or a Hilbert space representation until the final step, in which correlation functions are computed.