Irreducible Cartesian tensors
type: Item
instance of: scholarly article
title: Irreducible Cartesian tensors
zbMATH Open document ID: 1392.53001
DOI: 10.1515/9783110564860
author: R. F. Snider
published in: De Gruyter Studies in Mathematical Physics
publication date: 2017-11-14T00:00:00Z
review text: From a geometrical point of view, a three-dimensional Cartesian tensor is an object which depends on two or more directions. This book studies such objects and their rotational properties, in particular those which are irreducible under the three-dimensional rotation group. The monograph is based on papers written by J. A. R. Coope and the author, together with some generalisations and developments. It is written primarily with the needs and interests of physicists, chemists and other physical scientists in mind. Concepts are clearly explained and the presentation draws mainly on physical concepts, rather than the definition, theorem and proof approach used in mathematical presentations. The book emphasises almost exclusively the coordinate-free representation of vectors and tensors. It is essentially self-contained and includes an appendix on some formalities of linear algebra, which covers both the mathematical and physical way of defining certain terms. It contains a comprehensive introduction, followed by ten chapters. The final chapter gives some applications to quantum mechanics. The book contains a bibliography and although it does not have an index, a useful index of symbols is provided. Chapter 2 gives an introduction to vectors and tensors from a physical viewpoint. The unit second-order tensor and the Levi-Civita tensor are introduced. Properties of rotations in two dimensions are then studied. It is shown how a rotation can be described in terms of a tensor. The diagrammatic representation of a rotation tensor is introduced and this method of representation is then used throughout the book. The chapter goes on to study rotations in three dimensions and the three-dimensional rotation group. The objective of Chapter 3 is to study how a tensor behaves under a rotation and describes how it is often possible to reduce the tensor into rotationally independent parts. If no further reduction is possible, these parts are irreducible representations of the rotatio…
reviewed by: Anthony D. Osborne
Mathematics Subject Classification ID: 53-02
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 81-01
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 15-02
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 15A66
zbMATH DE Number: 6806643
zbMATH Keywords: three-dimensional rotation group
zbMATH Keywords: unit second-order tensor
zbMATH Keywords: Levi-Civita tensor
zbMATH Keywords: diagrammatic representation
zbMATH Keywords: irreducible representation
zbMATH Keywords: reduction
zbMATH Keywords: Legendre polynomial
zbMATH Keywords: tensor integral
zbMATH Keywords: spherical tensor
zbMATH Keywords: 3-\(j\) coupling tensor
zbMATH Keywords: Wigner's 3-\(j\) symbols
zbMATH Keywords: 6-\(j\) symbols
zbMATH Keywords: 9-\(j\) symbols
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/9783110564860
OpenAlex ID: W4240666250
description: scientific article; zbMATH DE number 6806643