We analyze the recently proposed classical/quantum mechanical interpretation of Zernike system and establish its equivalence to the Higgs oscillator on sphere or pseudosphere (Lobachevsky plane). We show that the non-reality of the classical Zernike Hamiltonian is an insignificant artifact of imaginary gauge and can be eliminated with a canonical transformation. The quantum counterpart of this canonical transformation is a similarity transformation mapping the system to the quantum Higgs oscillator with integration measure depending on [Formula: see text] parameters. When [Formula: see text], it results in the Hermitian Hamiltonian describing a free particle on (pseudo)sphere, while deviation from this point leads to a pseudo-Hermitian system.
We conjecture the connection between sl and so members of universal, in Vogel's sense, multiplets. The key element is the notion of the vertical componentwise sum circle plus v of Young diagrams. Representations in the decomposition of the power of the adjoint representation of sl(N) algebra can be parameterized by a pair of Young diagrams lambda and tau of equal area. We conjecture that within each universal multiplet there exists an associated pair of sl and so representations such that the Young diagram of the so representation is given by lambda circle plus v tau. This correspondence allows us to derive the universal form of the Casimir eigenvalues on that multiplet. We verify this conjecture for universal decompositions of tensor powers of the adjoint representations up to the fourth power, and for several series of universal representations. Based on this evidence, we propose a set of universal Casimirs for the fifth tensor power of the adjoint representation.We also conjecture that the vertical sum operation is connected with the (dual version of the) folding map of Dynkin diagrams. This connection may explain the intrinsic symmetry of universal formulae under automorphisms of Dynkin diagrams.
We consider eigenvalues of the Casimir operator on the naturally defined stable sequences of representations of su(N) algebra and prove that eigenvalues are linear over N iff λ_1+2λ_2+...+kλ_k=λ_N-1+2λ_N-2+...+kλ_N-k, where λ_i are Dynkin labels, and λ_i=0 for k<i<N-k, with fixed k. These representations are exactly those which appear in the decomposition of ad(su(N))^⊗ k, therefore this linearity admits the presentation of eigenvalues in the universal, in Vogel's sense, form, and supports the hypothesis of universal decomposition of ad^⊗ k into Casimir eigenspaces.
Thunderstorm Ground Enhancements (TGEs) are bursts of high-energy particle fluxes detected at Earth's surface, linked to the Relativistic Runaway Electron Avalanche (RREA) mechanism within thunderclouds. Accurate detection of TGEs is vital for advancing atmospheric physics and radiation safety, but event selection methods heavily rely on expert-defined thresholds. In this study, we use an automated supervised classification approach on a newly curated dataset of 2024 events from the Aragats Space Environment Center (ASEC). By combining a Tabular Prior-data Fitted Network (TabPFN) with SHAP-based interpretability, we attain 94.8% classification accuracy with 96% precision for TGEs. The analysis reveals data-driven thresholds for particle flux increases and environmental parameters that closely match the empirically established criteria used over the last 15 years. Our results demonstrate that modest but concurrent increases across multiple particle detectors, along with strong near-surface electric fields, are reliable indicators of TGEs. The framework we propose offers a scalable method for automated, interpretable TGE detection, with potential uses in real-time radiation hazard monitoring and multi-site atmospheric research.
The top-quark Yukawa coupling is extracted from the distribution of the top-quark pair ( tt ) invariant mass in proton-proton collisions using 140 fb−1 of data at √(s)=13 TeV collected in 2015–2018 by the ATLAS experiment at the Large Hadron Collider. In the region near the production threshold, the tt invariant mass spectrum is sensitive to electroweak virtual corrections, including contributions from Higgs boson exchange, thereby providing sensitivity to the top-quark Yukawa coupling. This is the first measurement in ATLAS that aims to obtain this coupling exploiting this approach. The tt system is reconstructed in the single-lepton final state, requiring exactly one isolated electron or muon and at least four jets with at least two identified as originating from b-quarks. The measured Yukawa coupling is found to be in good agreement with the Standard Model prediction. An upper limit on the top-quark Yukawa coupling strength of Yt < 2.1 relative to the Standard Model prediction is observed at 95
