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Spinors, Pseudo-Quaternions, and Orthogonal Groups


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1 University of Sydney, Sydney, Australia
     

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By using explicit forms for the Clifford matrices in Vs a subsystem {Qu } of the Clifford algebra is devised which is an orthogonal (rotation) group, i.e. QQT = 1, det Q = + 1. The matrices Qu (" pseudo-quaternions ") are in (1, 1) correspondence with vectors u of Vs which satisfy a certain quadratic condition (" spinors " ) , and in (2, 1) correspondence with the full rotation group of matrices A in V 4 The matrices A are given explicitly in terms of quadratic forms of spinors.
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  • Spinors, Pseudo-Quaternions, and Orthogonal Groups

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Authors

T. G. Room
University of Sydney, Sydney, Australia

Abstract


By using explicit forms for the Clifford matrices in Vs a subsystem {Qu } of the Clifford algebra is devised which is an orthogonal (rotation) group, i.e. QQT = 1, det Q = + 1. The matrices Qu (" pseudo-quaternions ") are in (1, 1) correspondence with vectors u of Vs which satisfy a certain quadratic condition (" spinors " ) , and in (2, 1) correspondence with the full rotation group of matrices A in V 4 The matrices A are given explicitly in terms of quadratic forms of spinors.