Hilbert Modules in Quantum Electro Dynamics and Quantum Probability
Hilbert Modules in Quantum Electro Dynamics and Quantum Probability
复制标题
量子电动力学和量子概率中的希尔伯特模块
DOI：
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发表时间：
1998
期刊：
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通讯作者：
Michael Skeide
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文献类型：
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作者：
Michael Skeide
翻译后摘要：一个物理系统的形式与一个杰出的状态可以描述在一个自然的方式上的希尔伯特模块。根据Accardi和Lu [1]的思想，我们把这种可能性应用到一个由真空态玻色子场和自由电子耦合组成的具体系统中，证明了这个物理系统可以用一种新的Fock模：对称Fock模来描述.原来，一个模块必须满足一个代数条件，以允许建设一个对称Fock modle.We证明在中心极限定理，在随机限制的集体运营商（即或多或少的时间积分相互作用哈密顿量）的时刻收敛到的时刻的自由创作者和零化子的一个完整的Fock模块。在Voiculescu [22]和Speicher [20]的意义下，这些算子在代数上形成自由白色噪声。
Abstract:A physical system of the form with a distinguished state on may be described in a natural way on a Hilbert -module. Following the ideas of Accardi and Lu [1], we apply this possibility to a concrete system consisting of a boson field in the vacuum state coupled to a free electron.We show that the physical system is described adequately on a new type of Fock module: the symmetric Fock module. It turns out that a module has to fulfill an algebraic condition in order to allow for the construction of a symmetric Fock module.We prove in a central limit theorem that in the stochastic limit the moments of the collective operators (i.e. more or less the time-integrated interaction Hamiltonian) converge to the moments of free creators and annihilators on a full Fock module. In the sense of Voiculescu [22] and Speicher [20] these operators form a free white noise over the algebra .