Schwinger’s oscillator realization of an SO(9) tensor operator

Schwinger’s oscillator realization of an SO(9) tensor operator The weights and representation matrices of the vector and the spinor representation of the Lie algebra SO(9) are introduced in the quantum mechanical language. Tensor product decompositions of any two of them are explicitly shown by using an algebraic method of quantum mechanics. Similar decompositions are finally achieved for a coupled tensor operator in the picture of Schwinger’s bosonic oscillators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png EPJ direct Springer Journals

Schwinger’s oscillator realization of an SO(9) tensor operator

EPJ direct , Volume 1 (1) – Jan 1, 2003

Schwinger’s oscillator realization of an SO(9) tensor operator

Eur Phys J C, EPJ C direct, 1 (2003) 003 EPJ C direct DOI 10.1140/epjcd/s2003-01-003-7 electronic only c Springer-Verlag 2003 Schwinger’s oscillator realization of an SO(9) tensor operator Teparksorn Pengpan Physics Department, Faculty of Science, Prince of Songkla University Hatyai 90112, Thailand pteparks@ratree.psu.ac.th Received: 13 Dec 2002 / Accepted: 21 Jan 2003 / Published online: 30 Jan 2003 Abstract. The weights and representation matrices of the vector and the spinor repre- sentation of the Lie algebra SO(9) are introduced in the quantum mechanical language. Tensor product decompositions of any two of them are explicitly shown by using an algebraic method of quantum mechanics. Similar decompositions are finally achieved for a coupled tensor operator in the picture of Schwinger’s bosonic oscillators. PACS: 02.20.Qs, 03.65.Fd, 04.65.+e, 12.60.Jv 1 Introduction The Lie algebra SO(9) which can be considered as the light-cone little group in eleven dimensions may play an important role in supergravity theory [1]. The aim of this paper is to perform calculation of the SO(9) tensor product decom- positions and to achive the similar decompositions in the picture of Schwinger’s bosonic oscillators in constructing the SO(9) representations. The method of calculation has been known for a long time, but the author would like to present it by using the quantum mechanical language. This paper is organized as follows. In Sect. 2, relevant basic facts of SO(9) are summarized to make the paper self-contained and to introduce the neces- sary notations and conventions. Explicit forms are presented of the SO(9) simple root and of Cartan subalgebra generators for vector and spinor representations. In Sect. 3, the SO(9) tensor product to produce the higher irreducible rep- resentations is explicitly calculated by using an algebraic method of quantum mechanics. In Sect. 4, after introducing the Schwinger’s bosonic oscillators for the SO(9) vector and...
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Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg
Subject
Physics; Physics, general; Particle and Nuclear Physics; Nuclear Physics, Heavy Ions, Hadrons; Particle Acceleration and Detection, Beam Physics; Nuclear Fusion; Atomic/Molecular Structure and Spectra
ISSN
1435-3725
D.O.I.
10.1140/epjcd/s2003-01-003-7
Publisher site
See Article on Publisher Site

Abstract

The weights and representation matrices of the vector and the spinor representation of the Lie algebra SO(9) are introduced in the quantum mechanical language. Tensor product decompositions of any two of them are explicitly shown by using an algebraic method of quantum mechanics. Similar decompositions are finally achieved for a coupled tensor operator in the picture of Schwinger’s bosonic oscillators.

Journal

EPJ directSpringer Journals

Published: Jan 1, 2003

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