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On The Existence of Local Observables in Theories With a Factorizing S-MatrixJuly 7th, 2004


The scaling limit of the two-dimensional Ising model above the critical temperature is considered as an example for relativistic quantum theories on two-dimensional Minkowski space exhibiting a factorizing S-matrix. In this model, a recently proposed criterion for the existence of local quantum field theories with a prescribed factorizing scattering matrix is verified, thereby establishing a new constructive approach to two-dimensional quantum field theory in a particular example. The existence proof is accomplished by analyzing nuclearity properties of certain specific subsets of Fermionic Fock spaces, and yields as a byproduct also a verification of the energy nuclearity condition of Buchholz and Wichmann in models of free Fermions in four space-time dimensions.

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