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arXiv · 1412.7802

Spinor Structure and Modulo 8 Periodicity

V. V. Varlamov
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Abstract

Spinor structure is understood as a totality of tensor products of biquaternion algebras, and the each tensor product is associated with an irreducible representation of the Lorentz group. A so-defined algebraic structure allows one to apply modulo 8 periodicity of Clifford algebras on the system of real and quaternionic representations of the Lorentz group. It is shown that modulo 8 periodic action of the Brauer-Wall group generates modulo 2 periodic relations on the system of representations, and all the totality of representations under this action forms a self-similar fractal structure. Some relations between spinors, twistors and qubits are discussed in the context of quantum information and decoherence theory.

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V. V. Varlamov. 2014-12-25. Spinor Structure and Modulo 8 Periodicity. https://arxiv.org/abs/1412.7802

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