In this talk, I will present the quantisation of the linear scalar field when the background spacetime metric is not smooth.
The analysis of quantum fields in spacetimes, where the metric is not smooth, has two main motivations. First, there are several models of physical phenomena that require spacetime metrics with finite regularity. Second, the analysis of the well-posedness of Einstein's equations, viewed as a system of hyperbolic PDEs requires spaces with finite regularity.
I will focus mainly on the microlocal aspects of the causal propagator and the two-point function of ground states and the techniques used to overcome the lack of smoothness.
The talk will be based on arXiv:1910.13789 and arXiv:2207.01429.