Abstract
Lorentz invariance, local commutativity, and the absence of negative mass states imply that the vacuum expectation value and the Fourier transform of the retarded commulator of a product of field operators are boundary values of analytic functions. The cases of four and five local scalar fields are investigated in the spirit of the approach of Källén and Wightman. It is shown that the domain of analyticity of the vacuum expectation value in x-space contains that of there retarted commutator in p-space. A computation of the real points of these domains is discussed in an appendix.
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