Haag's theorem

Haag's theorem

Rudolf Haag postulated [Haag, R: " [http://doc.cern.ch/cernrep/1955/1955-008/1955-008.html On quantum field theories] ", Matematisk-fysiske Meddelelser, 29, 12 (1955).] that the interaction picture does not exist in an interacting, relativistic quantum field theory, something now commonly known as Haag's Theorem. The theorem was subsequently proved by a number of different authors. It is, however, inconvenient as in the canonical development of perturbative quantum field theory - which includes quantum electrodynamics - cited as one of the great successes of modern science - the interaction picture is used throughout.

Citing the formulation used by Arageorgis [Arageorgis, A.: 1995, "Fields, Particles, and Curvature: Foundations and Philosophical Aspects of Quantum Field Theory in Curved Spacetime", Ph.D. Thesis, Univ. of Pittsburgh.] :

* If two pure ground states are not equal, then they generate unitarily inequivalent irreducible representations.
* If two local quantum fields are unitarily equivalent at any given time, then both fields are free if one of them is free.

References

Further reading

* John Earman, Doreen Fraser, "Haag's Theorem and Its Implications for the Foundations of Quantum Field Theory", Erkenntnis 64 (2006): 305-344, [http://philsci-archive.pitt.edu/archive/00002673/ online at philsci-archive]
* Doreen Fraser, "Haag’s Theorem and the Interpretation of Quantum Field Theories with Interactions", PhD thesis, U. of Pittsburgh, [http://etd.library.pitt.edu/ETD/available/etd-07042006-134120/ online]

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