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Haag’s Theorem and Successful Applications of Scattering Theory

September 26, 2012

Mike Miller

Haag’s theorem has been taken by some philosophers to establish that quantum field theory cannot consistently represent interacting fields. As all of our best theories in particle physics are interacting quantum field theories, this leads to the worry that our formalism for calculating with our best theories in particle physics is inconsistent. Earman and Fraser (2006) provides clarification of the significance of the theorem and an understanding of how it is possible to give mathematically consistent calculations in scattering theory despite the result. I will show that their analysis does not fully address a different worry raised by Haag’s theorem. In particular, I will argue that their approach does not fully address the concern that our claims about the empirical adequacy of quantum field theory are undermined by the theorem. Instead I will show that our empirical adequacy claims are protected from Haag’s result by the complex approximation schemes that are required to perform calculations of theoretical predictions for realistic experimental observables.

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