Finite dimensional models inspired by the perturbative algebraic quantum field theory (pAQFT) framework

学生将研究受摄动代数量子场论（pAQFT）框架启发的有限维模型，该框架用于构建洛伦兹流形上的量子场论模型。代替洛伦兹流形M，我们可以考虑一个因果集S，即一个具有偏序关系的集合，它模拟了一个因果结构（基于Rafael Sorkin的思想）。有充分的理由相信pAQFT可以在这样的结构上工作（可能经过一些修改），这可能是一个很好的玩具模型，用于测试可以应用于无限维度设置的想法。经典理论是EPSRC资助的夏季学生项目（Edmund Dable-Heath， 2016年夏季）的主题，结果表明存在一种自然的方法来构建S上的规范括号（即构建经典理论）。目前的博士项目将关注探索下一步：变形量化和重整化。

The student will work on finite dimensional models inspired by the perturbative algebraic quantum field theory (pAQFT) framework, which is framework used to construct models of quantum field theories on Lorentzian manifolds. Instead of a Lorentzian manifold M one can consider a causal set S, i.e. a set with a partial order relation that models a causal structure (based on ideas of Rafael Sorkin). There are strong reasons to believe that pAQFT can work on such structures (possibly with some modifications) and this could be a good toy model for testing ideas that can then be applied in the infinite dimensional setting. Classical theory was the topic of an EPSRC funded summer student project (of Edmund Dable-Heath, summer 2016) and the results indicate that there is a natural way to construct the canonical bracket on S (i.e. construct the classical theory). The current PhD project will concern exploring the next steps: deformation quantization and renormalization.