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Superspinors and Graded Lorentz Groups in Three, Four and Five Dimensions

✍ Scribed by J. Lukierski; A. Nowicki

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
988 KB
Volume
30
Category
Article
ISSN
0015-8208

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✦ Synopsis

Abstract

Three superalgebras osp(1; 2; F) (F = R, C, H) and corresponding three supergroups are considered. The transformation laws of spinors with anticommuting components for 3‐dimensional (O(2, 1) ≃ Sp(2; R)), 4‐dimensional (O(3, 1) ≃ Sp(2, C)) and 5‐dimensional (O(4, 1) ≃ Sp(2; H)) Lorentz group are extended in a supersymmetric way by introducing nonlinear realizations of the supergroups OSp(1, 2; F). The affine Grassmann spinors in all three cases are obtained by suitable β€œflat” limit of the nonlinear realization. Different gradings and different contractions of osp(1,2; F) (F = R, C, H) superalgebras are considered.

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