We give a rigorous definition of moments of an unbounded observable with respect to a quantum state in terms of Yosida's approximations of unbounded generators of contractions semigroups. We use this notion to characterize Gaussian states in terms of the moments of the field operator, which we call Weyl moments. As a by-product, rigorous formulae for the mean value vector and the covariance matrix of a Gaussian state are obtained.

中文翻译：

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Weyl 矩和量子高斯态

我们根据 Yosida 对收缩半群的无界生成元的近似，给出了关于量子态的无界可观测矩的严格定义。我们使用这个概念来根据场算符的矩来表征高斯状态，我们称之为外尔矩。作为副产品，获得了高斯状态的均值向量和协方差矩阵的严格公式。