Rudolf Haag postulated 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:
* 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.
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.
* 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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