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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.

highsciguy
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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

Urb
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Arnold Neumaier
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  • Thank you. I am familiar with the Kadanoff-Baym equations. I am – highsciguy Nov 18 '12 at 15:58
  • ... merely searching for the connection to conventional quantum field theory and the optical theorem as well as physical interpretations. – highsciguy Nov 18 '12 at 16:04
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    @highsciguy: The connection is given on the usual heuristic level by the CTP functional integral. - What physical interpretation are you looking for beyond knowing that the K-B equations give a dynamics for the correlation functions, hence tell something about the unstable particle spectrum? – Arnold Neumaier Nov 18 '12 at 16:10
  • Concerning physical interpretations I think of modified decay laws, Quantum Zeno effect and so on. Things which are usually discussed for individual particles. How may such effects be extracted from the statistical Kadanoff-Baym description or how can I understand it in terms of ordinary relativistic quantum mechanics. – highsciguy Nov 18 '12 at 16:26
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    @highsciguy: I haven't seen a single paper on work on the measurement problem based on nonequilibrium relativistic QFT. Thus this looks like (difficult) unexplored territory. The quasiparticle content depends on the state, and measurement should probably be modelled in terms of suitable initial conditions and external forces. But the questions asked in the two communities are too different to relate them easily. - For the interpretation of unstable particles (resonances) as poles of the S-matrix in ordinary QM, see, e.g., Vol. 3 of Thirrings course on mathematical physics. – Arnold Neumaier Nov 18 '12 at 17:21