Time-Ordered Products in Two-Dimensional Field Theories

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Abstract
It is shown that the vacuum expectation values (VEV) of ⋮eλσ⋮(t,f)=∫dxf(x) ⋮eλσ⋮(t,x) are continuous functions of the time for test functions which are C∞ and of rapid decrease, with λ in some neighborhood of the origin in the complex plane. The field σ(x) is the pseudopotential derived from the pseudovector current of a free two-component massive field in two-dimensional space-time. A consequence of this result is the existence of Green's functions in the Federbush model. An essential technique in the proof is a theorem by Jaffe on the boundary values of limits of sequences of analytic functions.

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