Publications

Order by: publication date number of citations

• An algebraic approach to intertwined quantum phase transitions in the Zr isotopes

  Noam Gavrielov

  SciPost Phys. Proc. 14, 028 (2023) · published 24 November 2023 | Toggle abstract · pdf

  The algebraic framework of the interacting boson model with configuration mixing is employed to demonstrate the occurrence of intertwined quantum phase transitions (IQPTs) in the $_{40}$Zr isotopes with neutron number 52-70. The detailed quantum and classical analyses reveal a QPT of crossing normal and intruder configurations superimposed on a QPT of the intruder configuration from U(5) to SU(3) and a crossover from SU(3) to SO(6) dynamical symmetries.

• New perspectives in gravity-mediated supersymmetry breaking

  Robin Ducrocq

  SciPost Phys. Proc. 14, 027 (2023) · published 24 November 2023 | Toggle abstract · pdf

  New solutions in supersymmetry breaking through gravity mediation have been recently discovered. Such solutions have interesting properties regarding renormalisation and introduce new contributions in the scalar potential that may help to resolve some issues of the Standard Model. The purpose of this article is to investigate the consequences of these new structures. We construct a model related to these new solutions, the S2MSSM, and present some preliminary results on the effects of these new contributions, especially on the Standard Model's Higgs boson mass.

• Linking ladder operators for the Rosen-Morse and Pöschl-Teller systems

  Simon Garneau-Desroches, Véronique Hussin

  SciPost Phys. Proc. 14, 026 (2023) · published 24 November 2023 | Toggle abstract · pdf

  An analysis of the realizations of the ladder operators for the Rosen-Morse and Pöschl-Teller quantum systems is carried out. The failure of the algebraic method of construction in the general Rosen-Morse case is exposed and explained. We present the reduction of a recently obtained set of $(2n ± 1)$-th-order Rosen-Morse ladder operators to the usual first-order realization for the Pöschl-Teller case known in the literature.

• On old relations of Lie theory, classical geometry and gauge theory

  Rolf Dahm

  SciPost Phys. Proc. 14, 025 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Having been led by hadron interactions and low-energy photoproduction to SU(4) and non-compact SU*(4) symmetry, the general background turned out to be projective geometry (PG) of $P^3$, or when considering line and Complex geometry to include gauge theory, aspects of $P^5$. Point calculus and its dual completion by planes introduced quaternary (quadratic) "invariants" $x_{\mu}x^{\mu}=0$ and $p_{\mu}p^{\mu}=0$, and put focus on the intermediary form $(xu)$ and its treatment. Here, the major result is the identification of the symmetric 20 of SU(4) comprising nucleon and Delta states as related to the quaternary cubic forms discussed by Hilbert in his work on full invariant systems. So PG determines geometrically the scene by representations (reps) and invariant theory without having to force affine restrictions and additional (spinorial or gauge) rep theory.

• Newton mechanics, Galilean relativity, and special relativity in $\alpha$-deformed binary operation setting

  Won S. Chung, Mahouton N. Hounkonnou

  SciPost Phys. Proc. 14, 024 (2023) · published 23 November 2023 | Toggle abstract · pdf

  We define new velocity and acceleration having dimension of $(Length)^{\alpha}/(Time)$ and $(Length)^{\alpha}/(Time)^2,$ respectively, based on the fractional addition rule. We discuss the formulation of fractional Newton mechanics, Galilean relativity and special relativity in the same setting. We show the conservation of the fractional energy, characterize the Lorentz transformation and group, and derive the expressions of the energy and momentum. The two body decay is discussed as a concrete illustration.

• Generalized Heisenberg-Weyl groups and Hermite functions

  Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo

  SciPost Phys. Proc. 14, 023 (2023) · published 23 November 2023 | Toggle abstract · pdf

  A generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with respect to the orientation of the axes, are properly included in the structure of this new family of groups. Generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of these new groups, are introduced.

• Generalisation of affine Lie algebras on compact real manifolds

  Rutwig Campoamor-Stursberg, Marc de Montigny, Michel Rausch de Traubenberg

  SciPost Phys. Proc. 14, 022 (2023) · published 23 November 2023 | Toggle abstract · pdf

  We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.

• Hilbert space structure and classical limit of the low energy sector of U(N) quantum Hall ferromagnets

  Manuel Calixto, Alberto Mayorgas, Julio Guerrero

  SciPost Phys. Proc. 14, 021 (2023) · published 23 November 2023 | Toggle abstract · pdf

  Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify and construct the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites. The carrier Hilbert space of irreducible representations of U(N) is described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N-M). Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.

• The tower of Kontsevich deformations for Nambu-Poisson structures on $\mathbb{R}^d$: Dimension-specific micro-graph calculus

  Ricardo Buring, Arthemy V. Kiselev

  SciPost Phys. Proc. 14, 020 (2023) · published 23 November 2023 | Toggle abstract · pdf

  In Kontsevich's graph calculus, internal vertices of directed graphs are inhabited by multi - vectors, e.g., Poisson bi - vectors; the Nambu - determinant Poisson brackets are differential - polynomial in the Casimir(s) and density $\varrho$ times Levi - Civita symbol. We resolve the old vertices into subgraphs such that every new internal vertex contains one Casimir or one Levi - Civita symbol×$\varrho$. Using this micro - graph calculus, we show that Kontsevich's tetrahedral $\gamma_3$-flow on the space of Nambu - determinant Poisson brackets over $\mathbb{R}^3$ is a Poisson coboundary: we realize the trivializing vector field $\vec{X}$ over $\mathbb{R}^3$ using micro - graphs. This $\vec{X}$ projects to the known trivializing vector field for the $\gamma_3$-flow over $\mathbb{R}^2$.

• Renormalizable extension of the Abelian Higgs-Kibble model with a dim.6 derivative operator

  Daniele Binosi, Andrea Quadri

  SciPost Phys. Proc. 14, 019 (2023) · published 23 November 2023 | Toggle abstract · pdf

  We present a new approach to the consistent subtraction of a non power-counting renormalizable extension of the Abelian Higgs-Kibble (HK) model supplemented by a dim. 6 derivative-dependent operator controlled by the parameter $z$. A field-theoretic representation of the physical Higgs scalar by a gauge-invariant variable is used in order to formulate the theory by exploiting a novel differential equation, controlling the dependence of the quantized theory on $z$. These results pave the way to the consistent subtraction by a finite number of physical parameters of some non-power-counting renormalizable models possibly of direct relevance to the study of the Higgs potential at the LHC.