Quaternion-valued integral representations of the harmonic electromagnetic and spinor fields
type: Item
instance of: scholarly article
title: Quaternion-valued integral representations of the harmonic electromagnetic and spinor fields
zbMATH Open document ID: 0945.30037
author: O. Diekmann
published in: Doklady Mathematics
publication date: 2000-10-08T00:00:00Z
review text: Let \(\mathbb{Q}\) be a set of complex quaternions, \(a\in\mathbb{Q}\) and \(D_a: =D+M^a\), where \(D\) is the Dirac operator and \(M^af=fa\). Then the equation \(D_a f=0\) for \(\mathbb{Q}\)-valued function \(f\in C^1(G)\), \(G\subset\mathbb{R}^3\) is (an equivalent notation) the generalized Moisil-Theodoresku system, considered by \textit{V. V. Kravchenko} and \textit{M. V. Shapiro} [Dokl. Akad. Nauk Ross. Akad. Nauk, 329, No. 5, 547-549 (1993)]. The author proves that the solutions of \(D_af=0\) are connected with the harmonic electromagnetic and spinor fields. For them he obtains the Cauchy integral formula and the Sokhotskij formulas.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 1050647
zbMATH Keywords: spinor field
zbMATH Keywords: complex quaternions
zbMATH Keywords: Dirac operator
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1050647