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arXiv · 2401.10324

Biquaternions, Majorana spinors and time-like spin-foams

José Diogo Simão
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Abstract

This work is developed in the context of Lorentzian spin-foams with space- and time-like boundaries. It is argued that the equations describing the semiclassical regime of the various spin-foam amplitudes admit a common biquaternionic structure. A correspondence is given between Majorana 2-spinors and time-like surfaces in Minkowski 3-space based on such complexified quaternions. A symplectic structure for Majorana spinors is constructed, with which the unitary representation theory of $\mathrm{SU}(1, 1)$ is re-derived. As the main result, we propose a symplectomorphism between Majorana spinor space (with an area constraint) and $T^*\mathrm{SU}(1, 1)$, generalizing previous studies on twisted geometries to the case of time-like 2-surfaces.

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José Diogo Simão. 2024-01-18. Biquaternions, Majorana spinors and time-like spin-foams. https://arxiv.org/abs/2401.10324

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