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arXiv · 2311.06328

Poincare group spin networks

M. V. Altaisky
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Abstract

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.

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M. V. Altaisky. 2024-06-05. Poincare group spin networks. https://doi.org/10.1007/s10773-024-05688-7

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