Poincare group spin networks
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914824115453952 |
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| author | Altaisky, M. V. |
| author_facet | Altaisky, M. V. |
| contents | Spin network technique is usually generalized to relativistic case by changing $SO(4)$ group -- Euclidean counterpart of the Lorentz group -- to its universal spin covering $SU(2)\times SU(2)$, or by using the representations of $SO(3,1)$ Lorentz group. We extend this approach by using inhomogeneous Lorentz group $\mathcal{P}=SO(3,1)\rtimes \mathbb{R}^4$, which results in the simplification of the spin network technique. The labels on the network graph corresponding to the subgroup of translations $\mathbb{R}^4$ make the intertwiners into the products of $SU(2)$ parts and the energy-momentum conservation delta functions. This maps relativistic spin networks to usual Feynman diagrams for the matter fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06328 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Poincare group spin networks Altaisky, M. V. General Relativity and Quantum Cosmology Spin network technique is usually generalized to relativistic case by changing $SO(4)$ group -- Euclidean counterpart of the Lorentz group -- to its universal spin covering $SU(2)\times SU(2)$, or by using the representations of $SO(3,1)$ Lorentz group. We extend this approach by using inhomogeneous Lorentz group $\mathcal{P}=SO(3,1)\rtimes \mathbb{R}^4$, which results in the simplification of the spin network technique. The labels on the network graph corresponding to the subgroup of translations $\mathbb{R}^4$ make the intertwiners into the products of $SU(2)$ parts and the energy-momentum conservation delta functions. This maps relativistic spin networks to usual Feynman diagrams for the matter fields. |
| title | Poincare group spin networks |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2311.06328 |