Integral representations for Schwinger functionals and the moment problem over nuclear spaces
Integral representations for Schwinger functionals and the moment problem over nuclear spaces
复制标题
施温格泛函的积分表示和核空间的矩问题
DOI：
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
J. Yngvason
中科院分区：
文献类型：
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作者：
H. Borchers;J. Yngvason
结果表明，交换核 * 代数上的连续正线性泛函当且仅当泛函为强正（即所有正多项式为正）时才可积分分解为字符。当应用于核测试函数空间上的对称张量代数时，这为欧几里得量子场论的施温格函数成为对偶空间上连续圆柱测度的矩提供了充分必要条件。另一个应用是将怀特曼函数分解为具有簇属性的状态的问题。
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.