Symmetric analogues of Rarita-Schwinger equations
type: Item
instance of: scholarly article
title: Symmetric analogues of Rarita-Schwinger equations
zbMATH Open document ID: 1025.58013
DOI: 10.1023/A:1014923601006
published in: Annals of Global Analysis and Geometry
publication date: 2002-05-12T00:00:00Z
review text: The Dirac operator and twisted Dirac operators have been studied extensively during the last decades and were used in many other branches of mathematics and mathematical physics. Rarta-Schwinger equation is the spin analogue of Dirac equation in dimension 4. In the paper under review, a generalization of the classical Rarita-Schwinger equations for spin 3/2 fields to the case of spin fields with values in irreducible representation spaces with weight \(k+1/2\) is given. First, a suitable definition of the Rarita-Schwinger operator on any Riemannian manifold is settled and its properties with respect to the conformal group action are studied. The corresponding first order systems are elliptic and their fundamental solution is constructed. The representation character of polynomial solutions of these equations on a flat space and their relationships are described in details.
reviewed by: Ion Mihai
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1738876
zbMATH Keywords: conformally invariant first order operators
zbMATH Keywords: twisted Dirac operator
zbMATH Keywords: spherical monogenics
zbMATH Keywords: Rarita-Schwinger operator
author: J. Bureš
author: Frank Sommen
author: Vladimír Souček
author: Peter van Lancker
MaRDI profile type: Publication
full work available at URL: a:1014923601006
OpenAlex ID: W205392407
description: scientific article; zbMATH DE number 1738876