Hermitian Pre-Hurwitz Pairs and the Minkowski Space

Shôji Kanemaki and Osamu Suzuki
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Shôji Kanemaki: Science University of Tokyo, Department of Mathematics
Osamu Suzuki: College of Humanities and Sciences Nihon University, Department of Mathematics

A chapter in Deformations of Mathematical Structures, 1989, pp 225-232 from Springer

Abstract: Abstract A. Hurwitz introduced pairs (ℝn,ℝp) of Euclidean spaces, each of which possesses the property = (x ∈ ℝn, y ∈ ℝp) for a bilinear mapping f: ℝn × ℝp → ℝn for 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.

Keywords: Minkowski Space; Complex Matrice; Clifford Algebra; Twistor Space; Bilinear Mapping (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-2643-1_21

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DOI: 10.1007/978-94-009-2643-1_21

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