Publications

Order by: publication date number of citations

• 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.

  1 citation

• Comments on the negative grade KdV hierarchy

  Y. F. Adans, Jose F. Gomes, G. V. Lobo, A. H. Zimerman

  SciPost Phys. Proc. 14, 014 (2023) · published 23 November 2023 | Toggle abstract · pdf

  The construction of negative grade KdV hierarchy is proposed in terms of a Miura-gauge transformation. Such gauge transformation is employed within the zero curvature representation and maps the Lax operator of the mKdV into its couterpart within the KdV setting. Each odd negative KdV flow is obtained from an odd and its subsequent even negative mKdV flows. The negative KdV flows are shown to inherit the two different vacua structure that characterizes the associated mKdV flows.

  1 citation

• Replica method for eigenvalues of real Wishart product matrices

  Jacob A. Zavatone-Veth, Cengiz Pehlevan

  SciPost Phys. Core 6, 026 (2023) · published 5 April 2023 | Toggle abstract · pdf

  We show how the replica method can be used to compute the asymptotic eigenvalue spectrum of a real Wishart product matrix. For unstructured factors, this provides a compact, elementary derivation of a polynomial condition on the Stieltjes transform first proved by Müller [IEEE Trans. Inf. Theory. 48, 2086-2091 (2002)]. We then show how this computation can be extended to ensembles where the factors are drawn from matrix Gaussian distributions with general correlation structure. For both unstructured and structured ensembles, we derive polynomial conditions on the average values of the minimum and maximum eigenvalues, which in the unstructured case match the results obtained by Akemann, Ipsen, and Kieburg [Phys. Rev. E 88, 052118 (2013)] for the complex Wishart product ensemble.

  1 citation

• Relativistic kinematics in flat and curved space-times

  Patrick Moylan

  SciPost Phys. Proc. 14, 037 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Almost immediately after the seminal papers of Poincaré (1905,1906) and Einstein (1905) on special relativity, wherein Poincaré established the full covariance of the Maxwell-Lorentz equations under the scale-extended Poincaré group and Einstein explained the Lorentz transformation using his assumption that the one-way speed of light in vacuo is constant and the same for all inertial observers (Einstein's second postulate), attempts were made to get at the Lorentz transformations from basic properties of space and time but avoiding Einstein's second postulate. Various such approaches usually involve general consequences of the relativity principle, such as a group structure to the set of all admissible inertial transformations and also assumptions about causality and/or homogeneity of space-time combined with isotropy of space. The first such attempt is usually attributed to von Ignatowsky in 1911. It was followed shortly thereafter by a paper of Frank and Rothe published in the same year. Since then, papers have continued to be written on the subject even up to the present. We elaborate on some of the results of such papers paying special attention to a 1968 paper of Bacri and Lévy-Leblond where possible kinematical groups include the de Sitter and anti-de Sitter groups and lead to special relativity in de Sitter and anti-de Sitter spaces.

• Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators

  Guner Muarem

  SciPost Phys. Proc. 14, 038 (2023) · published 24 November 2023 | Toggle abstract · pdf

  In this paper we use the canonical complex structure $\mathbb{J}$ on $\mathbb{R}^{2n}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold. Moreover, we prove that the algebra of these Dirac operators is isomorphic to the Lie algebra $\mathfrak{su}(1,2)$ which leads to the Howe dual pair $(U(n),\mathfrak{su}(1,2))$.

• Wigner function analysis of finite matter-radiation systems

  Eduardo Nahmad-Achar, Ramón López-Peña, Sergio Cordero, Octavio Castaños Garza

  SciPost Phys. Proc. 14, 039 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of minimum fidelity.

• Group theoretical derivation of consistent particle theories

  Giuseppe Nisticò

  SciPost Phys. Proc. 14, 040 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories can be derived through a strictly deductive development from the principle of relativistic invariance and position covariance, also with anti-unitary space inversion and unitary time reversal operators. In doing so the class of possible consistent theories is extended for positive but also zero mass particles. In particular, consistent theories for a Klein-Gordon particle are derived and the non-localizability theorem for a non zero helicity massless particle is extended.

• On Möbius gyrogroup and Möbius gyrovector space

  Kurosh Mavaddat Nezhaad, Ali Reza Ashrafi

  SciPost Phys. Proc. 14, 041 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Gyrogroups are new algebraic structures that appeared in 1988 in the study of Einstein's velocity addition in the special relativity theory. These new algebraic structures were studied intensively by Abraham Ungar. The first gyrogroup that was considered into account is the unit ball of Euclidean space $\mathbb{R}^3$ endowed with Einstein's velocity addition. The second geometric example of a gyrogroup is the complex unit disk $\mathbb{D}$={z ∈ $\mathbb{C}: |z|<1$}. To construct a gyrogroup structure on $\mathbb{D}$, we choose two elements $z_1, z_2 ∈ \mathbb{D}$ and define the Möbius addition by $z_1\oplus z_2 = \frac{z_1+z_2}{1+\bar{z_1}z_2}$. Then $(\mathbb{D},\oplus)$ is a gyrocommutative gyrogroup. If we define $r \odot x$ $=$ $\frac{(1+|x|)^r - (1-|x|)^r}{(1+|x|)^r + (1-|x|)^r}\frac{x}{|x|}$, where $x ∈ \mathbb{D}$ and $r ∈ \mathbb{R}$, then $(\mathbb{D},\oplus,\odot)$ will be a real gyrovector space. This paper aims to survey the main properties of these Möbius gyrogroup and Möbius gyrovector space.

• Clocking mechanism from a minimal spinning particle model

  Tobiasz Pietrzak, Łukasz Bratek

  SciPost Phys. Proc. 14, 042 (2023) · published 24 November 2023 | Toggle abstract · pdf

  The clock hypothesis plays an important role in the theory of relativity. To test this hypothesis, a mechanical model of an ideal clock is needed. Such a model should have the phase of its intrinsic periodic motion increasing linearly with the affine parameter of the clock's center of mass worldline. A class of relativistic rotators introduced by Staruszkiewicz in the context of an ideal clock is studied. A singularity in the inverse Legendre transform leading from the Hamiltonian to the Lagrangian leads to new possible Lagrangians characterized by fixed values of mass and spin. In free motion the rotators exhibit intrinsic motion with the speed of light and fixed frequency.

• Segal's contractions, AdS and conformal groups

  Daniel Sternheimer

  SciPost Phys. Proc. 14, 043 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Symmetries and their applications always played an important role in I.E. Segal's work. I shall exemplify this, starting with his correct proof (at the Lie group level) of what physicists call the "O'Raifeartaigh theorem", continuing with his incidental introduction in 1951 of the (1953) Inönü-Wigner contractions, of which the passage from AdS (SO(2,3)) to Poincaré is an important example, and with his interest in conformal groups in the latter part of last century. Since the 60s Flato and I had many fruitful interactions with him around these topics. In a last section I succintly relate these interests in symmetries with several of ours, especially elementary particles symmetries and deformation quantization, and with an ongoing program combining both.