arXiv subjects

Zhanna Kuznetsova

Publications and source records attributed to Zhanna Kuznetsova.

13 recordsLinked to original sources

arXiv2026

Regular Black Hole Formation and Gamma-Ray Burst from Matter Conversion

During the gravitational collapse of a massive star into a regular black hole, a new form of matter must be produced in order to prevent the formation of a central singularity. Since such matter is not present in the initial stellar configuration, it must emerge dynamically during the collapse. This formation process is expected to be accompanied by a strong release of energy in the form of electromagnetic radiation, which may be observable. Here we investigate the gravitational collapse of baryonic matter into Dymnikova-Hayward-Bardeen regular black holes. We estimate the radiation density and the corresponding bolometric luminosity generated by the formation of the matter sector responsible for singularity avoidance. We show that such processes provide a possible mechanism for gamma-ray bursts. Moreover, compatibility with gamma-ray burst requires small regularization effects. As a result, the corresponding regular black holes differ weakly from the Schwarzschild black hole.

gr-qc↗

arXiv2026

Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework

We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups $Z_3^2$, $Z_2^p\times Z_3^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum paraoscillators. In the Rittenberg-Wyler's color Lie (super)algebras framework the above abelian groups are the simplest ones which induce mixed brackets interpolating commutators and anticommutators. These mixed brackets allow to accommodate two types of parastatistics: one based on the permutation group (beyond bosons and fermions in any space dimension) and an anyonic parastatistics based on the braid group. In both such cases the two broad classes of paraparticles are given by parabosons and parafermions. Mixed-bracket parafermions are created by nilpotent operators; they satisfy a generalized Pauli exclusion principle leading to roots-of-unity truncations in their multi-particle energy spectrum (braided Majorana qubits and their Gentile-type parastatistics are recovered in this color Lie superalgebra setting). Mixed-bracket parabosons do not admit truncations of the spectrum; the minimal detectable signature of their parastatistics is encoded in the measurable probability density of two indistinguishable parabosonic oscillators in a given energy eigenstate.

math-ph↗

arXiv2025

Integrable $\mathbb{Z}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories

In this paper we present a general framework to construct integrable $\mathbb{Z}_2^2$-graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and Sinh-Gordon models; they are based on $\mathbb{Z}_2^2$-graded color Lie algebras and their fields satisfy a parabosonic statististics. The mathematical tools here introduced are the $\mathbb{Z}_2^2$-graded covariant extensions of the Lax pair formalism and of the Polyakov's soldering procedure. The $\mathbb{Z}_2^2$-graded Sinh-Gordon model is derived from an affine $\mathbb{Z}_2^2$-graded color Lie algebra, mimicking a procedure originally introduced by Babelon-Bonora to derive the ordinary Sinh-Gordon model. The color Lie algebras under considerations are: the $6$-generator $\mathbb{Z}_2^2$-graded $sl_2$, the $\mathbb{Z}_2^2$-graded affine ${\widehat{sl_2}}$ algebra with two central extensions, the $\mathbb{Z}_2^2$-graded Virasoro algebra obtained from a Hamiltonian reduction.

math-ph↗

arXiv2023

Beyond the $10$-fold way: $13$ associative $Z_2\times Z_2$-graded superdivision algebras

The "$10$-fold way" refers to the combined classification of the $3$ associative division algebras (of real, complex and quaternionic numbers) and of the $7$, ${\mathbb Z}_2$-graded, superdivision algebras (in a superdivision algebra each homogeneous element is invertible). The connection of the $10$-fold way with the periodic table of topological insulators and superconductors is well known. Motivated by the recent interest in ${\mathbb Z}_2\times{\mathbb Z}_2$-graded physics (classical and quantum invariant models, parastatistics) we classify the associative ${\mathbb Z}_2\times {\mathbb Z}_2$-graded superdivision algebras and show that $13$ inequivalent cases have to be added to the $10$-fold way. Our scheme is based on the "alphabetic presentation of Clifford algebras", here extended to graded superdivision algebras. The generators are expressed as equal-length words in a $4$-letter alphabet (the letters encode a basis of invertible $2\times 2$ real matrices and in each word the symbol of tensor product is skipped). The $13$ inequivalent ${\mathbb Z}_2\times {\mathbb Z}_2$-graded superdivision algebras are split into real series ($4$ subcases with $4$ generators each), complex series ($5$ subcases with $8$ generators) and quaternionic series ($4$ subcases with $16$ generators).

math-ph↗

arXiv2021

Classification of minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie (super)algebras and some applications

This paper presents the classification, over the fields of real and complex numbers, of the minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie algebras and Lie superalgebras spanned by $4$ generators and with no empty graded sector. The inequivalent graded Lie (super)algebras are obtained by solving the constraints imposed by the respective graded Jacobi identities. A motivation for this mathematical result is to systematically investigate the properties of dynamical systems invariant under graded (super)algebras. Recent works only paid attention to the special case of the one-dimensional ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Poincaré superalgebra. As applications, we are able to extend certain constructions originally introduced for this special superalgebra to other listed ${\mathbb Z}_2\times{\mathbb Z}_2$-graded (super)algebras. We mention, in particular, the notion of ${\mathbb Z_2}\times{\mathbb Z}_2$-graded superspace and of invariant dynamical systems (both classical worldline sigma models and quantum Hamiltonians). As a further byproduct we point out that, contrary to ${\mathbb Z}_2\times{\mathbb Z}_2$-graded superalgebras, a theory invariant under a ${\mathbb Z}_2\times{\mathbb Z}_2$-graded algebra implies the presence of ordinary bosons and three different types of exotic bosons, with exotic bosons of different types anticommuting among themselves.

math-ph↗

arXiv2019

On Light-like Deformations of the Poincaré Algebra

We investigate the observational consequences of the light-like deformations of the Poincaré algebra induced by the jordanian and the extended jordanian classes of Drinfel'd twists. Twist-deformed generators belonging to a Universal Enveloping Algebra close nonlinear algebras. In some cases the nonlinear algebra is responsible for the existence of bounded domains of the deformed generators. The Hopf algebra coproduct implies associative nonlinear additivity of the multi-particle states. A subalgebra of twist-deformed observables is recovered whenever the twist-deformed generators are either hermitian or pseudo-hermitian with respect to a common invertible hermitian operator.

hep-th↗

arXiv2013

Effects of Twisted Noncommutativity in Multi-particle Hamiltonians

The noncommutativity induced by a Drinfel'd twist produces Bopp-shift like transformations for deformed operators. In a single-particle setting the Drinfel'd twist allows to recover the noncommutativity obtained from various methods which are not based on Hopf algebras. In multi-particle sector, on the other hand, the Drinfel'd twist implies novel features. In conventional approaches to noncommutativity, deformed primitive operators are postulated to act additively. A Drinfel'd twist implies non-additive effects which are controlled by the coproduct. We illustrate these features for a class of (abelian twist-deformed) 2D Hamiltonians. Suitable choices of the parameters lead to the Hamiltonian of the noncommutative Quantum Hall Effect, the harmonic oscillator, the quantization of the configuration space. The non-additive effects in the multi-particle sector, leading to results departing from the existing literature, are pointed out.

hep-th↗

arXiv2011

D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics

The linear (homogeneous and inhomogeneous) (k, N, N-k) supermultiplets of the N-extended one-dimensional Supersymmetry Algebra induce D-module representations for the N=2,4,8 superconformal algebras. For N=2, the D-module representations of the A(1,0) superalgebra are obtained. For N=4 and scaling dimension λ=0, the D-module representations of the A(1,1) superalgebra are obtained. For $λ\neq 0$, the D-module representations of the D(2,1;α) superalgebras are obtained, with $α$ determined in terms of the scaling dimension $λ$ according to: $α=-2λ$ for k=4, i.e. the (4,4) supermultiplet, $α=-λ$ for k=3, i.e. (3,4,1), and $α=λ$ for k=1, i.e. (1,4,3). For $λ\neq 0$ the (2,4,2) supermultiplet induces a D-module representation for the centrally extended sl(2|2) superalgebra. For N=8, the (8,8) root supermultiplet induces a D-module representation of the D(4,1) superalgebra at the fixed value $λ=1/4$. A Lagrangian framework to construct one-dimensional, off-shell, superconformal invariant actions from single-particle and multi-particles D-module representations is discussed. It is applied to explicitly construct invariant actions for the homogeneous and inhomogeneous N=4 (1,4,3) D-module representations (in the last case for several interacting supermultiplets of different chirality).

hep-th↗

arXiv2010

Extended Supersymmetric Quantum Mechanics of Fierz and Schur Type

We discuss two independent constructions to introduce an N-extended Supersymmetric Quantum Mechanics. The first one makes use of the Fierz identities while the second one (divided into two subcases) makes use of the Schur lemma. The N supercharges Q_I are square roots of a free Hamiltonian H given by the tensor product of a D-dimensional Laplacian and a 2d-dimensional identity matrix operator. We present the mutual relations among N, D and d. The mod 8 Bott's periodicity of Clifford algebras is encoded, in the Fierz case, in the Radon-Hurwitz function and, in the Schur case, in an extra independent function.

math-ph↗

arXiv2007

Decomposition and Oxidation of the N-Extended Supersymmetric Quantum Mechanics Multiplets

We furnish an algebraic understanding of the inequivalent connectivities (computed up to $N\leq 10$) of the graphs associated to the irreducible supermultiplets of the N-extended Supersymmetric Quantum Mechanics. We prove that the inequivalent connectivities of the N=5 and N=9 irreducible supermultiplets are due to inequivalent decompositions into two sets of N=4 (respectively, N=8) supermultiplets. "Oxido-reduction" diagrams linking the irreducible supermultiplets of the N=5,6,7,8 supersymmetries are presented. We briefly discuss these results and their possible applications.

hep-th↗

arXiv2007

Refining the classification of the irreps of the 1D N-Extended Supersymmetry

The linear finite irreducible representations of the algebra of the 1D $N$-Extended Supersymmetric Quantum Mechanics are discussed in terms of their "connectivity" (a symbol encoding information on the graphs associated to the irreps). The classification of the irreducible representations with the same fields content and different connectivity is presented up to $N\leq 8$.

hep-th↗

arXiv2006

Superalgebras of (split-)division algebras and the split octonionic M-theory in (6,5)-signature

The connection of (split-)division algebras with Clifford algebras and supersymmetry is investigated. At first we introduce the class of superalgebras constructed from any given (split-)division algebra. We further specify which real Clifford algebras and real fundamental spinors can be reexpressed in terms of split-quaternions. Finally, we construct generalized supersymmetries admitting bosonic tensorial central charges in terms of (split-)division algebras. In particular we prove that split-octonions allow to introduce a split-octonionic M-algebra which extends to the (6,5) signature the properties of the 11-dimensional octonionic M-algebras (which only exist in the (10,1) Minkowskian and (2,9) signatures).

hep-th↗

arXiv2005

Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained generalized supersymmetries admit a dual formulation. For both real and complex spinors generalized supersymmetries are constructed and classified as dimensional reductions of supersymmetries from {\em oxidized} space-times (i.e. the maximal space-times associated to $n$-component Clifford irreps). We apply these results to sistematically construct a class of models describing superparticles in presence of bosonic tensorial central charges, deriving the consistency conditions for the existence of the action, as well as the constrained equations of motion. Examples of these models (which, in their twistorial formulation, describe towers of higher-spin particles) were first introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and Lukierski (for complex spinors).

hep-th↗