Chapter

Reality properties of spinors

Adam M. Bincer

in Lie Groups and Lie Algebras

Published in print October 2012 | ISBN: 9780199662920
Published online January 2013 | e-ISBN: 9780191745492 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199662920.003.0006
Reality properties of spinors

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Reality properties of spinors are described by defining conjugate, self-conjugate and complex representations. Two types of self-conjugate representations are identified and named orthogonal and symplectic. It is shown that the semispinors of so(8k) and the spinors of so(8k±1) are orthogonal, the semispinors of so(8k±2) are complex, and the spinors of so(8k±3) and the semispinor of so(8k+4) are symplectic.

Keywords: spinor; semispinor; conjugate; complex; orthogonal; symplectic

Chapter.  1610 words. 

Subjects: Mathematical and Statistical Physics

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