Weyl $C^*$ -代数的多项式扩张
Polynomial extensions of the Weyl $C^*$-algebra
摘要：
我们引入高阶（多项式）扩展的唯一（同构）非平凡中心扩展的海森堡代数。利用后者的玻色子表示，我们构造了Weyl $C^*$ -代数的相应多项式模拟，并利用这个结果导出了一维Heisenberg群的相关推广的合成律的显式形式.这些结果被用来计算真空特征函数以及伽利略代数中观测量的矩。这些对象的连续扩展给出了一种新的二次量子化，即使在二次量子化的情况下，它也与二次福克函子完全不同。
英文摘要：
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the latter, we construct the corresponding polynomial analogue of the Weyl $C^*$-algebra and use this result to deduce the explicit form of the composition law of the associated generalization of the 1-dimensional Heisenberg group. These results are used to calculate the vacuum characteristic func- tions as well as the moments of the observables in the Galilei algebra. The continuous extensions of these objects gives a new type of second quantization which even in the quadratic case is quite different from the quadratic Fock functor.
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