Igor Salom

• Institute of Physics Belgrade

In essence, the COVID-19 pandemic can be regarded as a systems biology problem, with the entire world as the system, and the human population as the element transitioning from one state to another with certain transition rates. While capturing all the relevant features of such a complex system is hardly possible, compartmental epidemiological model...

Higher category theory can be employed to generalize the notion of a gauge group to the notion of a gauge n -group. This novel algebraic structure is designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus it generalizes the concept of gauge symmetry, giving rise to a...

We study whether it is possible to use high-p⊥ data/theory to constrain the temperature dependence of the shear viscosity over entropy density ratio η/s of the matter formed in ultrarelativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC). We use two approaches: (i) We calculate hi...

We consider the problem of including a finite number of scattering centers in dynamical energy loss and classical DGLV formalism. Previously, either one or an infinite number of scattering centers were considered in energy loss models, while efforts to relax such approximations require a more conclusive and complete treatment. In reality, however,...

The ideas and results that are in the background of the 2022 Nobel Prize in physics had an immense impact on our understanding of reality. Therefore, it is crucial that these implications reach also the general public, not only the scientists in the related fields of quantum mechanics. The purpose of this review is to attempt to elucidate these rev...

While there has been much computational work on the effect of intervention measures, such as vaccination or quarantine, the influence of social distancing on the epidemics’ outbursts is not well understood. We present a realistic, analytically solvable, framework for COVID-19 dynamics in the presence of social distancing measures. The model is a ge...

We study whether it is possible to use high-$p_\perp$ data/theory to constrain the temperature dependence of the shear viscosity over entropy density ratio $\eta/s$ of the matter formed in ultrarelativistic heavy-ion collisions at the RHIC and LHC. We use two approaches: i) We calculate high-$p_\perp$ $R_{AA}$ and flow coefficients $v_2$, $v_3$ and...

We consider the problem of including a finite number of scattering centers in dynamical energy loss and classical DGLV formalism. Previously, either one or an infinite number of scattering centers were considered in energy loss calculations, while attempts to relax such approximations were largely inconclusive or incomplete. In reality, however, th...

Understanding sociodemographic factors behind COVID-19 severity relates to significant methodological difficulties, such as differences in testing policies and epidemics phase, as well as a large number of predictors that can potentially contribute to severity. To account for these difficulties, we assemble 115 predictors for more than 3,000 US cou...

We study the \( s\ell(2) \) Gaudin model with general boundary K-matrix in the framework of the algebraic Bethe ansatz. The off-shell action of the generating function of the \( s\ell(2) \) Gaudin Hamiltonians is determined without any restriction whatsoever on the boundary parameters.

Understanding sociodemographic factors behind COVID-19 severity relates to significant methodological difficulties, such as differences in testing policies and epidemics phase, as well as a large number of predictors that can potentially contribute to severity. To account for these difficulties, we assemble 115 predictors for more than 3000 US coun...

QGP tomography aims to constrain the QGP parameters by exploiting both low and high- p ⊥ theory and data. With this goal in mind, we present a fully optimised framework DREENA-A based on a state-of-the-art energy loss model. The framework can include any, in principle arbitrary, temperature profile within the dynamical energy loss formalism. Thus,...

Global Health Security Index (GHSI) categories are formulated to assess the capacity of world countries to deal with infectious disease risks. Thus, higher values of these indices were expected to translate to lower COVID-19 severity. However, it turned out to be the opposite, surprisingly suggesting that higher estimated country preparedness to ep...

Quark-gluon plasma (QGP) tomography aims to constrain the parameters characterizing the properties and evolution of QGP formed in heavy-ion collisions, by exploiting low- and high-p⊥ theory and data. Higher-order harmonics vn (n>2) are an important—but seldom explored—part of this approach. However, to take full advantage of them, several issues ha...

The emergence of a new virus variant is generally recognized by its usually sudden and rapid spread (outburst) in a certain world region. Due to the near-exponential rate of initial expansion, the new strain may not be detected at its true geographical origin but in the area with the most favorable conditions leading to the fastest exponential grow...

Global Health Security Index (GHSI) categories are formulated to assess the capacity of world countries to deal with infectious disease risks. Thus, higher values of these indices were expected to translate to lower COVID-19 severity. However, it turned out to be the opposite, surprisingly suggesting that higher estimated country preparedness to ep...

QGP tomography aims to constrain the parameters characterizing the properties and evolution of Quark-Gluon Plasma (QGP) formed in heavy-ion collisions, by exploiting low and high-$p_\perp$ theory and data. Higher-order harmonics $v_n$ ($n>2$) are an important -- but seldom explored -- part of this approach. However, to take full advantage of them,...

We study the so(3) Gaudin model with general boundary K-matrix in the framework of the algebraic Bethe ansatz. The off-shell action of the generating function of the so(3) Gaudin Hamiltonians is determined. The proof based on the mathematical induction is presented on the algebraic level without any restriction whatsoever on the boundary parameters...

While there has been much computational work on the effect of intervention measures, such as vaccination or quarantine, the influence of social distancing on the epidemics' outbursts is not well understood. We present a realistic, analytically solvable, framework for COVID-19 dynamics in the presence of social distancing measures. The model is a ge...

Understanding variations in the severity of infectious diseases is essential for planning proper mitigation strategies. Determinants of COVID-19 clinical severity are commonly assessed by transverse or longitudinal studies of the fatality counts. However, the fatality counts depend both on disease clinical severity and transmissibility, as more inf...

We present a fully optimised framework DREENA-A based on a state-of-the-art energy loss model. The framework can include any, in principle arbitrary, temperature profile within the dynamical energy loss formalism. Thus, 'DREENA' stands for Dynamical Radiative and Elastic ENergy loss Approach, while 'A' stands for Adaptive. DREENA-A does not use fit...

Identifying the main environmental drivers of SARS‐CoV‐2 transmissibility in the population is crucial for understanding current and potential future outbursts of COVID‐19 and other infectious diseases. To address this problem, we concentrate on the basic reproduction number R0, which is not sensitive to testing coverage and represents transmissibi...

Determinants of COVID-19 clinical severity are commonly assessed by transverse or longitudinal studies of the fatality counts. However, the fatality counts depend both on disease clinical severity and transmissibility, as more infected also lead to more deaths. Moreover, fatality counts (and related measures such as Case Fatality Rate) are dynamic...

We present a comprehensive treatment of the non-periodic trigonometric sℓ(2) Gaudin model with triangular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. First, we give Bethe vectors of the non-periodic trigonometric sℓ(2) Gaudi...

Many studies have proposed a relationship between COVID-19 transmissibility and ambient pollution levels. However, a major limitation in establishing such associations is to adequately account for complex disease dynamics, influenced by e.g. significant differences in control measures and testing policies. Another difficulty is appropriately contro...

A number of models in mathematical epidemiology have been developed to account for control measures such as vaccination or quarantine. However, COVID-19 has brought unprecedented social distancing measures, with a challenge on how to include these in a manner that can explain the data but avoid overfitting in parameter inference. We here develop a...

In article 2000101 Magdalena Djordjevic, Marko Djordjevic and co‐workers report widespread dynamical signatures in COVID‐19 confirmed case counts. They show that these signatures provide important quantitative information for understanding the disease spread and for constraining or inferring key infection progression parameters. This can lead to a...

Many studies have proposed a relationship between COVID-19 transmissibility and ambient pollution levels. However, a major limitation in establishing such associations is to adequately account for complex disease dynamics, influenced by e.g. significant differences in control measures and testing policies. Another difficulty is appropriately contro...

Identifying the main environmental drivers of SARS-CoV-2 transmissibility in the population is crucial for understanding current and potential future outbursts of COVID-19 and other infectious diseases. To address this problem, we concentrate on basic reproduction number $R_0$, which is not sensitive to testing coverage and represents transmissibil...

Widespread growth signatures in COVID‐19 confirmed case counts are reported, with sharp transitions between three distinct dynamical regimes (exponential, superlinear, and sublinear). Through analytical and numerical analysis, a novel framework is developed that exploits information in these signatures. An approach well known to physics is applied,...

It is hard to overstate the importance of a timely prediction of the COVID-19 pandemic progression. Yet, this is not possible without a comprehensive understanding of environmental factors that may affect the infection transmissibility. Studies addressing parameters that may influence COVID-19 progression relied on either the total numbers of detec...

High p⊥ theory and data are commonly used to study high p⊥ parton interactions with QGP, while low p⊥ data and corresponding models are employed to infer QGP bulk properties. On the other hand, with a proper description of high p⊥ parton-medium interactions, high p⊥ probes become also powerful tomography tools, since they are sensitive to global QG...

Widespread growth signatures in COVID-19 confirmed case counts are reported, with sharp transitions between three distinct dynamical regimes (exponential, superlinear and sublinear). Through analytical and numerical analysis, a novel framework is developed that exploits information in these signatures. An approach well known to physics is applied,...

Timely prediction of the COVID-19 progression is not possible without a comprehensive understanding of environmental factors that may affect the infection transmissibility. Studies addressing parameters that may influence COVID-19 progression relied on either the total numbers of detected cases and similar proxies and/or a small number of analyzed...

High $p_\perp$ theory and data are commonly used to study high $p_\perp$ parton interactions with QGP, while low $p_\perp$ data and corresponding models are employed to infer QGP bulk properties. On the other hand, with a proper description of high $p_\perp$ parton-medium interactions, high $p_\perp$ probes become also powerful tomography tools, si...

We discuss the relativistic three-body harmonic oscillator problem, and show that in the extreme relativistic limit its energy spectrum is closely related to that of the non-relativistic three-body problem in the \(\varDelta \)-string potential, which blurs the distinction between relativistic and confinement effects. This, perhaps unexpected, feat...

Understanding properties of Quark-Gluon Plasma requires an unbiased comparison of experimental data with theoretical predictions. To that end, we developed the dynamical energy loss formalism which, in distinction to most other methods, takes into account a realistic medium composed of dynamical scattering centers. The formalism also allows making...

The longstanding problem to understand if, why, and how objective functioning of the brain gives rise to a subjective perspective has been, in the last few decades, commonly known as the hard problem of consciousness. However, due to the strictly subjective and qualitative character of subjective experience, it is difficult to get a firm grip on th...

Drastic difference in the COVID-19 infection and fatality counts, observed between Hubei (Wuhan) and other Mainland China provinces raised public controversies. To address if these data can be consistently understood, we develop a model that takes into account all main qualitative features of the infection progression under suppression measures, wh...

We study the elliptic Gaudin model as a quasi-classical limit of the XYZ Heisenberg spin chain with the most general K-matrix. In particular, we give the generating function of the Gaudin Hamiltonians with boundary terms. *

We obtain the non-unitary classical r-matrix of the spin 1 trigonometric Gaudin model with boundary terms. Starting from the R-matrix and corresponding K-matrix of the spin 1 2 XXZ Heisenberg chain the so-called fusion procedure yields the R and K matrices of the spin 1 XXZ Heisenberg chain. We demonstrate that the corresponding classical r and K m...

The "measurement problem" of quantum mechanics, and the "hard problem" of cognitive science are the most profound open problems of the two research fields, and certainly among the deepest of all unsettled conundrums in contemporary science in general. Occasionally, scientists from both fields have suggested some sort of interconnectedness of the tw...

The "measurement problem" of quantum mechanics, and the "hard problem" of cognitive science are the most profound open problems of the two research fields, and certainly among the deepest of all unsettled conundrums in contemporary science in general. Occasionally, scientists from both fields have suggested some sort of interconnectedness of the tw...

The "measurement problem" of quantum mechanics, and the "hard problem" of cognitive science are the most profound open problems of the two research fields, and certainly among the deepest of all unsettled conundrums in contemporary science in general. Occasionally, scientists from both fields have suggested some sort of interconnectedness of the tw...

In this paper, we presented our recently developed Dynamical Radiative and Elastic ENergy loss Approach (DREENA-C) framework, which is a fully optimized computational suppression procedure based on our state-of-the-art dynamical energy loss formalism in constant temperature finite size QCD medium. With this framework, we have generated, for the fir...

We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can be realized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to disper...

We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can be realized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to disper...

We overview our recently developed DREENA-C and DREENA-B frameworks, where DREENA (Dynamical Radiative and Elastic ENergy loss Approach) is a computational implementation of the dynamical energy loss formalism; C stands for constant temperature and B for the medium evolution modeled by Bjorken expansion. At constant temperature our predictions over...

Dynamical energy loss formalism allows generating state-of-the-art suppression predictions in finite size QCD medium, employing a sophisticated model of high-p⊥ parton interactions with QGP. We here report a major step of introducing medium evolution in the formalism though 1+1D Bjorken (“B”) expansion, while preserving all complex features of the...

The Gaudin model has been revisited many times, yet some important issues remained open so far. With this paper we aim to properly address its certain aspects, while clarifying, or at least giving a solid ground to some other. Our main contribution is establishing the relation between the off-shell Bethe vectors with the solutions of the correspond...

We study the low-lying parts of the spectrum of three-quark states with definite permutation symmetry bound by an area-dependent three-quark potential. Such potentials generally confine three quarks in non-collinear configurations, but classically allow for free (unbound) collinear motion. We use our previous work to evaluate the low-lying parts of...

A recent paper "Single-world interpretations of quantum theory cannot be self-consistent" [arXiv:1604.07422] by D. Frauchiger and R. Renner has attracted a considerable interest of a broader physics audience and shortly elicited a number of replies. In spite of the objections that ensued, we find that significant part of the controversial initial c...

We apply the newly developed theory of permutation-symmetric O(6) hyperspherical harmonics to the quantum-mechanical problem of three nonrelativistic quarks confined by a spin-independent three-quark potential. We use our previously derived results to reduce the three-body Schrödinger equation to a set of coupled ordinary differential equations in...

Our dynamical energy loss formalism, allows generating state-of-the-art suppression predictions in finite size QCD medium. The formalism uses a sophisticated model of high-$p_\perp$ parton interactions with QGP, but simple medium model with constant temperature was assumed. We here present a newly developed DREENA-B framework, which abolishes the c...

In this paper, we presented our recently developed DREENA-C framework, which is a fully optimized computational suppression procedure based on our state-of-the-art dynamical energy loss formalism in constant temperature finite size QCD medium. With this framework, we for the first time, generated joint $R_{AA}$ and $v_2$ predictions within our dyna...

We apply the newly developed theory of permutation-symmetric O(6) hyperspherical harmonics to the quantum-mechanical problem of three non-relativistic quarks confined by a spin-independent 3-quark potential. We use our previously derived results to reduce the three-body Schr\"odinger equation to a set of coupled ordinary differential equations in t...

We study the open deformed XXX spin chain. In particular we obtain the explicit expression of the Sklyanin monodromy matrix in terms of the entries of the local Lax operator of the Jordanian chain. These results are essential in the study of the so-called quasi-classical limit of the system.

In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Skly...

In the derivation of the generating function of the Gaudin Hamiltonians with boundary terms, we follow the same approach used previously in the rational case, which in turn was based on Sklyanin's method in the periodic case. Our derivation is centered on the quasi-classical expansion of the linear combination of the transfer matrix of the XXZ Heis...

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, use...

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, use...

We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D). We label the state vectors according to the S3⊗SO(3)rot⊂O(2)⊗SO(3)rot⊂U(3)⋊S2⊂O(6) subgroup chain, where S3 is the three-body permutation group and S2 is its two element subg...

We have constructed the three-body permutation symmetric O(6) hyperspherical harmonics which can be used to solve the non-relativistic three-body Schrödinger equation in three spatial dimensions. We label the states with eigenvalues of the \(U(1) \otimes SO(3)_{rot} \subset U(3) \subset O(6)\) chain of algebras and we present the corresponding \(K...

We continue the study of positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R). We present the full list of these UIRs. We give the Proof of the case osp(1|8,R).

We continue the study of positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R). We present the full list of these UIRs. We give the Proof of the case osp(1|8,R).

We have constructed the three-body permutation symmetric O(6) hyperspherical harmonics which can be used to solve the non-relativistic three-body Schr{\" o}dinger equation in three spatial dimensions. We label the states with eigenvalues of the $U(1) \otimes SO(3)_{rot} \subset U(3) \subset O(6)$ chain of algebras and we present the corresponding $...

We construct the three-body permutation symmetric hyperspherical harmonics based on the subgroup chain S3 ⊗ SO (3)rot ⊂ O(2) ⊗ SO (3)rot ⊂ O(6) (and the subalgebra chain u(1) ⊗ so(3)rot ⊂ u(3) ⊂ so(6)). These hyperspherical harmonics represent a natural basis for solving non-relativistic three-body Schrodinger equation in three spatial dimensions....

We continue the study of positive energy (lowest weight) unitary irreducible representations of the superalgebras $osp(1|2n,R)$. We update previous results and present the full list of these UIRs. We give also some character formulae for these representations.

We define new creation operators relevant for implementation of the algebraic Bethe ansatz for the sℓ(2) Gaudin model with the general reflection matrix. This approach is based on the linear bracket corresponding to the relevant non-unitary classical r-matrix

Following Sklyanin's proposal in the rational case, we derive the generating function of the Gaudin Hamiltonians in the trigonometric case. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the inhomogeneous XXZ Heisenberg spin chain and the central element, the so-called Sklyanin determina...

Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The correspondin...

It is well known that the symmetric group has an important role (via Young tableaux formalism) both in labelling of the representations of the unitary group and in construction of the corresponding basis vectors (in the tensor product of the defining representations). We show that orthogonal group has a very similar role in the context of positive...

Orthosymplectic osp(1|2n) supersymmetry (alternative names: Generalized conformal supersymmetry with tensorial central charges, conformal M-algebra, parabose algebra) has been considered as an alternative to d-dimensional conformal superalgebra. Due to mathematical difficulties, even classification of its unitary irreducible representations (UIR’s)...

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We expl...

We use the permutation symmetric hyperspherical three-body variables to cast the non-relativistic three-body Schrödinger equation in two dimensions into a set of (possibly decoupled) differential equations that define an eigenvalue problem for the hyper-radial wave function depending on an SO(4) hyper-angular matrix element. We express this hyper-a...

SL (n,R) and Diff (n,R) groups play a prominent role in various particle physics and gravity theories, notably in chromogravity (that models the IR region of QCD), gauge affine generalizations of general relativity, and pD-branes. Applications of these groups require a knowledge of their features and especially rely on the unitary irreducible repre...

It is well known that the symmetric group has an important role (via Young tableaux formalism) both in labelling of the representations of the unitary group and in construction of the corresponding basis vectors (in the tensor product of the defining representations). We show that orthogonal group has a very similar role in the context of positive...

The Gell-Mann Lie algebra decontraction formula was proposed as an inverse to the Inönü-Wigner contraction formula. We considered recently this formula in the content of the special linear algebras sl(n), of an arbitrary dimension. In the case of these algebras, the Gell-Mann formula is not valid generally, and holds only for some particular algebr...

We use O(4) ≃ O(3)×O(3) algebraic methods to calculate the energy-splitting pattern of the K = 2, 3 excited states of the Y-string in two dimensions. To this purpose we use the dynamical O(2) symmetry of the Y-string in the shape space of triangles and compare our results with known results in three dimensions and find qualitative agreement.

We use SU(2)×SU(2) algebraicmethods to calculate the energy-splitting pattern of the K=2,3 excited states of the Y-string in two dimensions. To this purpose we use the dynamical O(2) symmetry of the Y-string in the shape space of triangles and compare our results with known results in three dimensions and find qualitative agreement.

Green's ansatz is a well known method for construction of "unique vacuum" representations of parabose (parafermi) algebra. Exploiting a Clifford algebra variant of the Green's ansatz we construct unitary representations with vacuum state carrying arbitrary SU(n) representation (n being the number of parabose operator pairs).

In recent years, generalized (conformal) supersymmetry has raised a lot of interest, in various contexts. We review the subject from a non-standard algebraical and grouptheoretical viewpoint, offering also some new insights in the matter.

The so called Gell-Mann or decontraction formula is proposed as an algebraic expression inverse to the Inonu-Wigner Lie algebra contraction. It is tailored to express the Lie algebra elements in terms of the corresponding contracted ones. In the case of sl(n,R) and su(n) algebras, contracted w.r.t. so(n) subalgebras, this formula is generally not v...

The Gell-Mann (decontraction) formula is an expression designed as an inverse to the Inönü-Wigner Lie algebra contraction. Its merits are notable simplicity and a great potential significance for the Lie algebra/group representation theory, while its drawback is a lack of general validity as an operator expression. The applicability of Gell-Mann's...

The so called Gell-Mann formula, a prescription designed to provide an inverse to the Inonu-Wigner Lie algebra contraction, has a great versatility and potential value. This formula has no general validity as an operator expression. The question of applicability of Gell-Mann's formula to various algebras and their representations was only partially...

The so called Gell-Mann formula expresses the Lie algebra elements in terms of the corresponding Inonu-Wigner contracted ones. In the case of sl(n, R) and su(n) algebras contracted w.r.t. so(n) subalgebras, the Gell-Mann formula is generally not valid, and applies only in the cases of some algebra representations. A generalization of the Gell-Mann...

Analytic expressions for the Clebsch-Gordan (CG) coefficients of the SO(5) group that involve the 14-dimensional representation can be found in an old paper of M. K. F. Wong. A careful analysis yields that roughly 30% of the coefficients given in that paper are wrong. The correct analytic expressions for all SO(5) group CG coefficients containing t...

We consider generalized conformal supersymmetry constructed as parabose N = 4 algebra. It is shown that Green's ansatz representations have, in this context, natural interpretation as multi particle spaces. The simplest nontrivial representation is shown to correspond to a massless particle of arbitrary helicity, and some peculiar properties of thi...

We consider generalized conformal supersymmetry constructed as parabose N=4 algebra. It is shown that sacrificing of manifest Lorentz covariance leads to interpretation of the generalized conformal supersymmetry as a symmetry that contains, on equal footing, two “rotation” groups. The necessary symmetry breaking is briefly considered. A connection...

The SA(5,R) = T5 ∧ SL(5,R) group of the special affine transformations of the five dimensional space-time, and its universal (double) covering SA(5,R) = T5 ∧ SL(5,R) group, are considered in the fields of gravity and/or 4-branes. The homogenious SL(5,R) subgroup and its spinorial representations are essential for the construction of the relevant wo...

The so called Gell-Mann formula is an useful prescription that, in some cases, allows us to express algebra generators in terms of generators of the corresponding In̈on̈u-Wigner contracted algebra. We demonstrate that in the cases of the sl(3,R) and sl(4,R) algebras, the Gell-Mann formula applies only for some representations. We point out how to g...

The form of realistic space-time supersymmetry is fixed, by Haag-Lopuszanski-Sohnius theorem, either to the familiar form of Poincare supersymmetry or, in massless case, to that of conformal supersymmetry. We question necessity for such strict restriction in the context of theories with broken symmetries. In particular, we consider parabose N=4 alg...

In this paper we investigate a particular possibility to extend C(1,3) conformal symmetry using Heisenberg operators, and a related possibility to extend conformal supersymmetry using parabose operators. The symmetry proposed is of a simple mathematical form, as is the form of necessary symmetry breaking that reduces it to the conformal (super)symm...

The duality symmetry of free electromagnetic field is analyzed within an algebraic approach. To this end, the conformal $c(1,3)$ algebra generators are expressed as operators quadratic in some abstract operators $\kappa^\alpha$ and $\pi_\beta$ which satisfy Heisenberg algebra relations. It is then shown that the duality generator can also be expres...