Publications

Order by: publication date number of citations

• 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.

• Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz

  Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampé, Luc Vinet

  SciPost Phys. Proc. 14, 018 (2023) · published 23 November 2023 | Toggle abstract · pdf

  The computation of the entanglement entropy for inhomogeneous free fermions chains based on $q$-Racah polynomials is considered. The eigenvalues of the truncated correlation matrix are obtained from the diagonalization of the associated Heun operator via the algebraic Bethe Ansatz. In the special case of chains based on dual $q$-Hahn polynomials, the eigenvectors and eigenvalues are expressed in terms of symmetric polynomials evaluated on the Bethe roots.

• A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré

  Angel Ballesteros, Ivan Guitérrez-Sagredo, Francisco J. Herranz

  SciPost Phys. Proc. 14, 017 (2023) · published 23 November 2023 | Toggle abstract · pdf

  In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated coisotropic Poisson homogeneous spaces coming from a coboundary Lie bialgebra structure. The approach is illustrated by obtaining in an explicit form several noncommutative spaces from (3+1)D (A)dS and Poincaré coisotropic Lie bialgebras. In particular, we review the construction of the $\kappa$-Minkowski and $\kappa$-(A)dS spacetimes in terms of the cosmological constant L. Furthermore, we present all noncommutative Minkowski and (A)dS spacetimes that preserve a quantum Lorentz subgroup. Finally, it is also shown that the same setting can be used to construct the three possible 6D $\kappa$-Poincaré spaces of time-like worldlines. Some open problems are also addressed.

• Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications

  Naruhiko Aizawa

  SciPost Phys. Proc. 14, 016 (2023) · published 23 November 2023 | Toggle abstract · pdf

  We give a brief review on recent developments of $\mathbb{Z}_2^n$-graded symmetry in physics in which hidden $\mathbb{Z}_2^n$-graded symmetries and $\mathbb{Z}_2^n$-graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$-graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for ${\cal N} = 1, 2$ algebras is presented and as an application of the irreps, $\mathbb{Z}_2^2$-graded SUSY classical actions are constructed.