We consider possible quantum effects for infinite systems implied by variations of the multiplication law in the algebra of observables. Using the algebraic formulation of quantum theory, we study the behavior of states ω under changes in the defining relations of the canonical commutation relations (CCR-algebra). These defining relations of the multiplication law depend explicitly on the symplectic form σ, which encodes commutation relations of canonical field operators. We consider the change in this form given by simple rescaling of σ by a positive parameter h. We analyze to what extent changes in h preserve the original state space (this gives restrictions on the admissible changes in the scaling parameter h) and which properties have original quantum states ω as states on the new algebra. We answer such questions for the quasi-free states. We show that any universally invariant state can be interpreted as a convex combination of Fock states with different values of constant h. The second important class of states we study is the KMS-state; here, the rescaling alters in a nontrivial way the relevant dynamics. We also show that it is possible to go beyond the limits restricting the changes in h, but then one has to restrict the CCR-algebra to a subalgebra.

中文翻译：

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Weyl代数上具有变量乘法定律的状态的性质

我们考虑了由可观代数中的乘法定律变化所暗示的无限系统的可能量子效应。使用量子理论的代数公式，我们研究了标准换向关系（CCR-代数）的定义关系发生变化时状态ω的行为。乘法定律的这些定义关系明确取决于辛形式σ，该辛形式对规范场算子的交换关系进行编码。我们考虑通过对正参数h进行σ的简单重新缩放而给出的这种形式的变化。我们分析h的变化在多大程度上保留了原始状态空间（这限制了缩放参数h的允许变化）以及哪些性质具有原始量子态ω作为新代数上的态。我们针对准无状态回答此类问题。我们证明，任何普遍不变的状态都可以解释为具有不同常数h的Fock状态的凸组合。我们研究的第二类重要状态是KMS状态。在这里，重新缩放会以不平凡的方式改变相关动态。我们还表明，有可能超出限制h的变化的限制，但随后必须将CCR代数限制为子代数。