Negative-dimensional groups in quantum physics
Negative-dimensional groups in quantum physics
复制标题
量子物理学中的负维群
DOI：
10.1088/0305-4470/22/11/014
复制
发表时间：
1989
期刊：
影响因子：
--
通讯作者：
G. Dunne
中科院分区：
文献类型：
--
作者：
G. Dunne
作者表明，明确定义的负维经典群体在其行动的格拉斯曼表示空间，连同外尔的字符公式的格拉斯曼张量表示这样的群体，导致一个框架中，一些令人惊讶的“负维”性质的群论不变量自然出现。作为一个应用，他表明，光谱的格拉斯曼谐振子和格拉斯曼角动量有关的玻色子对应的一个简单的分析延续的层面。
The author shows that an explicit definition of negative-dimensional classical groups in terms of their action on Grassmann representation spaces, together with Weyl's character formula for the Grassmann tensorial representations of such groups, leads to a framework in which some surprising 'negative-dimensional' properties of group theoretic invariants arise naturally. As an application, he shows that the spectra of the Grassmann harmonic oscillator and of Grassmann angular momentum are related to their bosonic counterparts by a simple analytic continuation in the dimension.