arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 0705.3417quant-ph
收藏

关于粒子数与量子不可逆性的讨论

A discussion on particle number and quantum indistinguishability

Graciela Domenech, Federico Holik

摘要:

量子力学中的个体性概念与经典物理学中的个体性概念有着根本的区别,如E.薛定谔在理论的早期阶段指出。关于这一事实,一些作者认为量子力学没有自己的语言,因此,量子不可逆性从一开始就没有被纳入理论。然而,可以使用拟集理论(Q)用一阶语言来表示量子不可约性的概念。在这项工作中,我们表明,Q不能捕捉量子非个体性的最重要的特征之一,这是事实,即存在量子系统的粒子数是没有很好地定义。还给出了Q的一个公理化变体,其中拟序不是一个本原概念(对于一种称为有限拟集的拟集)。这一结果鼓励搜索的理论,其中的quasidinal,是一个次要的概念,代表未定义的一些quasisets,除了明确表明,在一套理论的集合真正难以区分的实体,quasidinal不一定是一个原始的概念。

英文摘要:

The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schroedinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑