Kinematical correlations via $κ$-Poincaré coproducts

• URL: http://arxiv.org/abs/2606.03004v1
• Date: Tue, 02 Jun 2026 01:21:42 GMT
• Title: Kinematical correlations via $κ$-Poincaré coproducts
• Abstract summary: We study a kinematical consequence of the Hopf-algebraic momentum composition law in $$-Minkowski spacetime.<n>In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by $P_$ can be expanded into distinct auxiliary branches.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a kinematical consequence of the Hopf-algebraic momentum composition law in $κ$-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues $P_μ$ are nonlinearly related to the ordered-plane-wave labels $p_μ$. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity $P_+\equiv P_0+P_4=κe^{p_0/κ}$ enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent $κ$-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by $P_μ$ can be expanded into distinct auxiliary branches. If $P_μ$ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables $p_μ$ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

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