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Haag's theorem

Rudolf Haag postulated[1] 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[2]:

* 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

1. ^ Haag, R: On quantum field theories, Matematisk-fysiske Meddelelser, 29, 12 (1955).

2. ^ Arageorgis, A.: 1995, Fields, Particles, and Curvature: Foundations and Philosophical Aspects of Quantum Field Theory in Curved Spacetime, Ph.D. Thesis, Univ. of Pittsburgh.

Further reading

* John Earman, Doreen Fraser, Haag's Theorem and Its Implications for the Foundations of Quantum Field Theory, Erkenntnis 64 (2006): 305-344, online at philsci-archive

* Doreen Fraser, Haag’s Theorem and the Interpretation of Quantum Field Theories with Interactions, PhD thesis, U. of Pittsburgh, online

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