The symplecton: A prototype for semi-simple graded Lie algebras

✍ Scribed by L. C. Biedenharn; J. D. Louck

• Publisher: Springer
• Year: 1976
• Tongue: English
• Weight: 166 KB
• Volume: 1
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00417609

✦ Synopsis

An elementary, physically motivated, example of a semi-simple graded Lie algebra (SSGLA) is shown to be given by the 'symplecton realization' of angular momentum [an associative, involutive, inner-product algebra whose characteristic polynomials realize the symplectic group Sp( 2)]. The Pais-Rittenberg result shows that the n-component symplecton realizes the most general, SSGLA, Sp(2n). Invariance techniques in quantum physics have been significantly extended in recent years by tile concept of'supersymmetry' (and 'supergauges') introduced by Wess and Zumino [ 1 ], and by Volkov and Soroka [2] ; supersymmetry involves linear transformations relating states of different