Biquaternions, Majorana spinors and time-like spin-foams
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909077167144960 |
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| author | Simão, José Diogo |
| author_facet | Simão, José Diogo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Biquaternions, Majorana spinors and time-like spin-foams Simão, José Diogo General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Biquaternions, Majorana spinors and time-like spin-foams |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.10324 |