I am looking for a resource that clearly exposes the concepts of a particle source and a particle detector in the context of Quantum Field theory. I want to understand Irreversibility in this context.

  • $\begingroup$ There is a study by J. Schwinger and the corresponding books called "Particles, Sources, and Fields". $\endgroup$ Oct 8, 2012 at 15:54
  • $\begingroup$ Do you know of any specific papers of Schwinger that discuss this. I dont have access to these books currently. $\endgroup$
    – Prathyush
    Oct 9, 2012 at 7:05

1 Answer 1


Typically one thinks of the sources as being at infinite past, and the detection at infinite future; then a reversible S-matrix description applies. For photons, a corresponding treatment of sources and detectors can be found in Mandel & Wolf's treatise on quantum optics. But their treatment doesn't give any hint on irreversibility.

[Edit] Detection is always irreversible; nothing counts as detected unless there is an irreversible record of it. There is no really good account from first principles how an irreversible detection event is achieved. From the 1999 article ''Some problems in statistical mechanics that I would like to see solved'' by Elliot Lieb https://doi.org/10.1016/S0378-4371(98)00517-2:

The measurement process in quantum mechanics is not totally understood, even after three quarters of a century of thought by the deepest thinkers. At some level, the problems of quantum mechanical measurement are related, distantly perhaps, to the problems of non-equilibrium statistical mechanics. Several models (e.g. the laser) indicate this, but the connection, if any, is unclear and I would like to see more light on the subject.

But see

A field theoretic discussion of irreversibility necessitates a statistical mechanics treatment. This more detailed modeling is done in practice in a hydrodynamic or kinetic approximation. They treat sources as generators of beams with an extended distribution in space or phase space, respectively. The dynamics of both descriptions is irreversible, and may be computed in terms of $k$-particle irreducible ($k$PI) Feynman diagrams for $k=1$ and $k=2$, respectively.

The kinetic description is based on the Kadanoff-Baym equations in the 2PI Schwinger-Keldysh (CTP) formalism. The Kadanoff-Baym equations are dynamical equations for the 2-particle Wightman functions and their ordered analoga, and are used in practice to model high energy heavy ion collision experiments. See, e.g.,
and the discussions in
Good reading on the Keldysh formalism
What is known about quantum electrodynamics at finite times?

The hydrodynamic description is based on the simpler 1PI approach, but it is (to my knowledge) used mainly theoretically; see, e.g.,
Reviews of Modern Physics 49, 435 (1977)
and the papers

  • $\begingroup$ Can you briefly explain what goes into these two approaches? I thought there would be a much simpler explanation, where one can understand sources as excitations of Atomic substances, and Detectors as reactions of Light sensitive atoms. $\endgroup$
    – Prathyush
    Oct 9, 2012 at 7:01
  • $\begingroup$ Oh, the latter can be found in Mandel & Wolf's treatise on quantum optics, but their treatment doesn't give any hint on irreversibility. I thought you were mainly interested in the latter. A discussion of the origins of irreversibility necessitates a statistical mechanics treatment. $\endgroup$ Oct 9, 2012 at 7:22
  • $\begingroup$ Detection(in this context a chemical reaction) is an irreversible process right? I will look into the both resources I found this statement very interesting "They treat sources as generators of beams with an extended distribution in space or phase space". How do they treat detectors? The papers you linked to are a little technical for me right now, But let me try working towards them. $\endgroup$
    – Prathyush
    Oct 9, 2012 at 7:55
  • $\begingroup$ Yes, detection is always irreversible. I added some references. $\endgroup$ Oct 9, 2012 at 9:43

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