Abstract
It is shown that a continuous positive linear functional on a commutative nuclear *-algebra has an integral decomposition into characters if and only if the functional is strongly positive, i.e. positive on all positive polynomials. When applied to the symmetric tensor algebra over a nuclear test function space this gives a necessary and sufficient condition for the Schwinger functions of Euclidean quantum field theory to be the moments of a continuous cylinder measure on the dual space. Another application is to the problem of decomposing a Wightman functional into states having the cluster property.
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Communicated by H. Araki
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Borchers, H.J., Yngvason, J. Integral representations for Schwinger functionals and the moment problem over nuclear spaces. Commun.Math. Phys. 43, 255–271 (1975). https://doi.org/10.1007/BF02345023
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DOI: https://doi.org/10.1007/BF02345023