Unstable particles and quantum field theory

Question

I am searching for not too old literature on the quantum description of unstable particles. I am referring to something beyond the ad-hoc S-matrix description based on the optical theorem common to textbooks such as those given by Peskin and Schröder or Weinberg etc. The book "Open Quantum Systems and Feynman Integrals" by Exner seems to go in this direction. But I find the formulation there very mathematical. Certainly it is possible to understand it but I am worried if I will get the connection to physics.

Answer 1

In relativistic QFT, unstable particles are defined by poles in the correlation functions, analytically continued to the second sheet.

Actual computations are usually done using Kadanoff-Baym equations, using the CTP (closed time pathy) formalism. See, e.g., https://arxiv.org/abs/0801.4324