Algebra spinor representation

LB. Frenkel, Spinor representations of affine Lie algebras, Proc. Natl. Acad. Sci. USA 77 (1980), 6303-6306. 

In order to address polarization/rotation modulation—not just static polarization/rotation—an algebra is required which can reduce the ambiguity of a static representation. Such an algebra which is associated with 2, r, and that reduces the ambiguity up to a sign ambiguity, is available in the twistor formalism [28]. In this formalism, polarization/rotation modulation can be accomodated, and a spinor, K, can be represented not only by a null direction indicated by 2, q, or C, but also a real tangent vector L indicated in Fig. 4. 

The symmetry group of relativity theory tells the story. For the irreducible representations of the Poincare group (of special relativity) or the Einstein group (of general relativity) obey the algebra of quaternions. The basis functions of the quaternions, in turn, are two-component spinor variables [17]. 

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