On the two-point functions of some integrable relativistic quantum field theories

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Abstract
Two-point functions associated with the Federbush, massless Thirring, and continuum Ising models and their boson analogs are studied. In the Thirring case it is shown that the fields do not define operator-valued distributions, while temperedness of the two-point Wightman function is proved in the Ising case and in the Federbush case for a certain range of coupling constants. By relating the short-distance singularity of the Schwinger functions to the high-energy behavior of the spectral measures it is shown the fields cannot be made to satisfy the CCR/CAR by a rescaling. In the fermionic Federbush case this breakdown of the CAR occurs in spite of the fact that the fields correspond to a local Lagrangian.

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