arXiv 1505.045282015-05-18math-phhep-thmath.GRmath.MP

量子力学中的数字微积分与有限群

Digital calculus and finite groups in quantum mechanics

Vladimir Garcia-Morales

备注：: 31 pages, 8 figures, submitted for publication

摘要：

通过在经典力学和量子力学的最近公式中引入的一个数字函数，我们给出了一种新的有限群的无限族的构造，包括交换群和非交换群，它们对理论物理、原子物理和分子物理都有重要意义.我们的建设是不是基于代数关系满足发电机，但在建立适当的法律组成，诱导组结构的有限集的非负整数（基数的集合是等于秩序的组），从而使计算与有限组相当简单。建立了有限群无限族的抽象合成律，包括所有循环群（及其直和），二面体群，双循环群和其它亚循环群，$p$符号置换的对称群和偶置换的交错群.给出了具体的例子来说明在每种情况下得到的合成定律的表达式。

英文摘要：

By means of a digit function that has been introduced in a recent formulation of classical and quantum mechanics, we provide a new construction of some infinite families of finite groups, both abelian and nonabelian, of importance for theoretical, atomic and molecular physics. Our construction is not based on algebraic relationships satisfied by generators, but in establishing the appropriate law of composition that induces the group structure on a finite set of nonnegative integers (the cardinal of the set being equal to the order of the group) thus making computations with finite groups quite straightforward. We establish the abstract laws of composition for infinite families of finite groups including all cyclic groups (and any direct sums of them), dihedral, dicyclic and other metacyclic groups, the symmetric groups of permutations of $p$ symbols and the alternating groups of even permutations. Specific examples are given to illustrate the expressions for the law of composition obtained in each case.

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。

摘要：

英文摘要：

相关论文