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1. Semi-classical limit of the Dirac equation in curved space and applications to strained and photonic graphene

   https://doi.org/10.1088/1751-8121/adb402  

   Fillion-Gourdeau, François; Lorin, Emmanuel; MacLean, Steve; Yang, Xu (March 2025, Journal of Physics A: Mathematical and Theoretical)

   Abstract The semi-classical regime of static Dirac matter is derived from the Dirac equation in curved space-time. The leading- and next-to-leading-order contributions to the semi-classical approximation are evaluated. While the leading-order yields classical equations of motion with relativistic Lorentz and a geometric forces related to space curvature, the next-to-leading-order gives a transport-like equation with source terms. We apply the proposed strategy to the simulation of electron propagation on strained graphene surfaces, as well as to the dynamics of edge states in photonic graphene. 

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2. A Lorentz-equivariant transformer for all of the LHC

   https://doi.org/10.21468/SciPostPhys.19.4.108  

   Brehmer, Johann; Bresó, Victor; de_Haan, Pim; Plehn, Tilman; Qu, Huilin; Spinner, Jonas; Thaler, Jesse (January 2025, SciPost Physics)

   We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over space-time and is equivariant under Lorentz transformations. The underlying architecture is a versatile and scalable transformer, which is able to break symmetries if needed. We demonstrate the power of L-GATr for amplitude regression and jet classification, and then benchmark it as the first Lorentz-equivariant generative network. For all three LHC tasks, we find significant improvements over previous architectures. 

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3. Scattering amplitudes for monopoles: pairwise little group and pairwise helicity

   https://doi.org/10.1007/JHEP08(2021)029  

   Csáki, Csaba; Hong, Sungwoo; Shirman, Yuri; Telem, Ofri; Terning, John; Waterbury, Michael (August 2021, Journal of High Energy Physics)

   A bstract On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S -matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding “pairwise helicity” is identified with the quantized “cross product” of charges, e 1 g 2 − e 2 g 1 , for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S -matrix elements, as well as the full partial wave decomposition for the 2 → 2 fermion-monopole S -matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed. 

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4. Yukawa-Lorentz symmetry in non-Hermitian Dirac materials

   https://doi.org/10.1038/s42005-024-01629-2  

   Juričić, Vladimir; Roy, Bitan (December 2024, Communications Physics)

   Abstract Lorentz space–time symmetry represents a unifying feature of the fundamental forces, typically manifest at sufficiently high energies, while in quantum materials it emerges in the deep low-energy regime. However, its fate in quantum materials coupled to an environment thus far remained unexplored. We here introduce a general framework of constructing symmetry-protected Lorentz-invariant non-Hermitian (NH) Dirac semimetals (DSMs), realized by invoking masslike anti-Hermitian Dirac operators to its Hermitian counterpart. Such NH DSMs feature purely real or imaginary isotropic linear band dispersion, yielding a vanishing density of states. Dynamic mass orderings in NH DSMs thus take place for strong Hubbard-like local interactions through a quantum phase transition, hosting a non-Fermi liquid, beyond which the system becomes an insulator. We show that depending on the internal Clifford algebra between the NH Dirac operator and candidate mass order-parameter, the resulting quantum-critical fluid either remains coupled with the environment or recovers full Hermiticity by decoupling from the bath, while always enjoying an emergent Yukawa-Lorentz symmetry in terms of a unique terminal velocity. We showcase the competition between such mass orderings, their hallmarks on quasi-particle spectra in the ordered phases, and the relevance of our findings for correlated designer NH Dirac materials. 

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5. Multivariate fidelities

   https://doi.org/10.1088/1751-8121/adc645  

   Nuradha, Theshani; Mishra, Hemant K; Leditzky, Felix; Wilde, Mark M (April 2025, Journal of Physics A: Mathematical and Theoretical)

   The bivariate classical fidelity is a widely used measure of the similarity of two probability distributions. There exist a few extensions of the notion of the bivariate classical fidelity to more than two probability distributions; herein we call these extensions multivariate classical fidelities, with some examples being the Matusita multivariate fidelity and the average pairwise fidelity. Hitherto, quantum generalizations of multivariate classical fidelities have not been systematically explored, even though there are several well known generalizations of the bivariate classical fidelity to quantum states, such as the Uhlmann and Holevo fidelities. The main contribution of our paper is to introduce a number of multivariate quantum fidelities and show that they satisfy several desirable properties that are natural extensions of those of the Uhlmann and Holevo fidelities. We propose several variants that reduce to the average pairwise fidelity for commuting states, including the average pairwisez-fidelities, the multivariate semi-definite programming (SDP) fidelity, and a multivariate fidelity inspired by an existing secrecy measure. The second one is obtained by extending the SDP formulation of the Uhlmann fidelity to more than two states. All of these variants satisfy the following properties: (i) reduction to multivariate classical fidelities for commuting states, (ii) the data-processing inequality, (iii) invariance under permutations of the states, (iv) its values are in the interval $[0,1]$; they are faithful, that is, their values are equal to one if and only if all the states are equal, and they satisfy orthogonality, that is their values are equal to zero if and only if the states are mutually orthogonal to each other, (v) direct-sum property, (vi) joint concavity, and (vii) uniform continuity bounds under certain conditions. Furthermore, we establish inequalities relating these different variants, indeed clarifying that all these definitions coincide with the average pairwise fidelity for commuting states. We also introduce another multivariate fidelity called multivariate log-Euclidean fidelity, which is a quantum generalization of the Matusita multivariate fidelity. We also show that it satisfies most of the desirable properties listed above, it is a function of a multivariate log-Euclidean divergence, and it has an operational interpretation in terms of quantum hypothesis testing with an arbitrarily varying null hypothesis. Lastly, we propose multivariate generalizations of Matsumoto’s geometric fidelity and establish several properties of them. 

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