Polarization-Free Generators and the S-Matrix

Details Polarization-Free Generators and the S-Matrix Polarization-Free Generators and the S-Matrix

2000-03-27

arxiv.org/abs/hep-th/0003243v2

Commun.Math.Phys. 219 (2001) 125-140

Physics

High Energy Physics

High Energy Physics - Theory

Dedicated to the memory of Harry Lehmann, 19 pages; revised version (proof of Lemma 3.4 corrected)

Scientific paper

10.1007/s002200100411

Polarization-free generators, i.e. ``interacting'' Heisenberg operators which are localized in wedge-shaped regions of Minkowski space and generate single particle states from the vacuum, are a novel tool in the analysis and synthesis of two-dimensional integrable quantum field theories. In the present article, the status of these generators is analyzed in a general setting. It is shown that such operators exist in any theory and in any number of spacetime dimensions. But in more than two dimensions they have rather delicate domain properties in the presence of interaction. If, for example, they are defined and temperate on a translation-invariant, dense domain, then the underlying theory yields only trivial scattering. In two-dimensional theories, these domain properties are consistent with non-trivial interaction, but they exclude particle production. Thus the range of applications of polarization-free generators seems to be limited to the realm of two-dimensional theories.

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