Some Continuous Field Quantizations, Equivalent to the C*-Weyl Quantization
Some Continuous Field Quantizations, Equivalent to the C*-Weyl Quantization
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一些连续场量化，相当于 C*-Weyl 量化
DOI：
10.2977/prims/1145475406
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发表时间：
2005
影响因子：
1.2
通讯作者：
A. Rieckers
中科院分区：
文献类型：
--
作者：
R. Honegger;A. Rieckers
从一个（可能是无限维的）预辛空间（E,）出发，研究了一类修正的Weyl量化。对于实普朗克参数~的每一个值，我们都有一个C*- weyl代数W(E,~)，它们共同构成了C*-代数的连续域，如前面所讨论的。对于~ = 0，我们构造了一个Frechet-Poisson代数，它密集地包含在W（E,0）中，作为要量子化的经典可观测值。量子化的Weyl元素用所谓的量子化因子来修饰，表示在特定情况下的正常排序。在对量化因子的某些假设下，量化映射可以推广到Frechet-Poisson代数。在Rieel和Landsman意义上，它构成了一个严格的连续变形量化，相当于Weyl量化。在正则和忠实的Hilbert空间表示中实现C*-代数量化映射导致无界域表达式的量化。
Starting from a (possibly infinite dimensional) pre-symplectic space (E, ), we study a class of modified Weyl quantizations. For each value of the real Planck parameter ~ we have a C*-Weyl algebra W(E,~ ), which altogether constitute a con- tinuous field of C*-algebras, as discussed in previous works. For ~ = 0 we construct a Frechet-Poisson algebra, densely contained in W(E,0), as the classical observables to be quantized. The quantized Weyl elements are decorated by so-called quantiza- tion factors, indicating the kind of normal ordering in specific cases. Under some assumptions on the quantization factors, the quantization map may be extended to the Frechet-Poisson algebra. It is demonstrated to constitute a strict and continu- ous deformation quantization, equivalent to the Weyl quantization, in the sense of Rieel and Landsman. Realizing the C*-algebraic quantization maps in regular and faithful Hilbert space representations leads to quantizations of the unbounded field expressions.