Irreducible Cartesian tensors of highest weight, for arbitrary order
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- 作者：S.R. Mane srmane001@gmail.com" class="auth_mail" title="E-mail the corresponding author
- 关键词：Irreducible Cartesian tensors ; Spherical tensors ; Group representation theory ; Laplace&ndash ; Beltrami operator ; Gegenbauer polynomials ; Polarized beams
- 刊名：Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
- 出版年：2016
- 出版时间：21 March 2016
- 年：2016
- 卷：813
- 期：Complete
- 页码：62-67
- 全文大小：256 K
文摘
A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n ), for dimensions n≥3.