Hermitian Pre-Hurwitz Pairs and the Minkowski Space
Hermitian Pre-Hurwitz Pairs and the Minkowski Space
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埃尔米特前赫尔维茨对和闵可夫斯基空间
DOI：
10.1007/978-94-009-2643-1_21
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
O. Suzuki
中科院分区：
文献类型：
--
作者：
Shōji Kanemaki;O. Suzuki
A. Hurwitz引入了欧氏空间对（n，n，p），每个欧氏空间对都具有性质<f（x，y），f（x，y）>= <x，x><y，y>（x ∈ n，y ∈ p）对于双线性映射f：对于某些正整数n和p，n× p → n。他证明了这些对决定了真实的数、复数、四元数和八元数的空间，特别是当n = p = 1，2，4，分别为8。本文引入了前赫维茨对和厄米特前赫维茨对的概念。利用量子场论中常见的Dirac γ-矩阵，证明了存在一个确定Minkowski空间的Hermitian pre-Hurwitz对.这表明，埃尔米特前赫维茨对将发挥重要作用，在数学和物理学。
A. Hurwitz introduced pairs (ℝn,ℝp) of Euclidean spaces, each of which possesses the property <f(x,y), f(x,y)>= <x,x><y,y> (x ∈ ℝn, y ∈ ℝp) for a bilinear mapping f: ℝn× ℝp→ ℝnfor some positive integers n and p. He showed that these pairs determine the spaces of real numbers, complex numbers, quaternions, and octonions if, in particular, n = p = l, 2, 4, and 8, respectively. Here concepts of pre-Hurwitz pairs and hermitian pre-Hurwitz pairs are newly introduced. It is shown that there exists a hermitian pre-Hurwitz pair which determines the Minkowski space, by making use of the Dirac γ-matrices which are familar in quantum field theory. This suggests that hermitian pre--Hurwitz pairs will play an important role in both mathematics and physics.