JLJerzy Lukierski
Jerzy Lukierski
*This is an algorithmically generated author record based on publicly available information.
Research Subjects
Research Interests
Jerzy Lukierski has a total of 148 co-authors. Here are the top co-authors by number of shared publications:
- Sergey Fedoruk
Joint Institute for Nuclear Research
24 shared publications - Andrzej Borowiec
Institute of Theoretical Physics, pl. M University of Wroc law Borna 9 50-204 Wroc law Poland
14 shared publications - Wojtek J. Zakrzewski
Department of Mathematical Sciences, University of Durham, Durham, U.K.
13 shared publications Anatol Nowicki
Institute of Physics, University of Zielona Góra, pl. Słowiański 6, 65-069 Zielona Góra, Poland
11 shared publications- Piotr Kosiński
Faculty of Physics and Applied Informatics University of Lodz Poland
10 shared publications - Igor Bandos
University of the Basque Country
8 shared publications
Latest Publications
- Open Access
- 31 July 2024
- Published by Sissa Medialab Srl
- Vol. 463, 247
Doubly $\kappa$-deformed Yang models, Born - selfdual $\kappa$-deformed quantum phase spaces and two generalizations of Yang models
Recently it was shown that by using two different realizations of $\hat{o}(1,4)$ Lie algebra one can describe one-parameter standard Snyder model and two-parameter $\kappa$-deformed Snyder model. In this paper, by using the generalized Born duality and Jacobi identities we obtain from the $\kappa$-deformed Snyder model the doubly $\kappa$-deformed Yang model which provides the new class of quantum relativistic phase spaces. These phase spaces contain as subalgebras the $\kappa$-deformed Minkowski space-time as well as quantum $\tilde{\kappa}$-deformed fourmomenta and are depending on five independent parameters. Such a large class of quantum phase spaces can be described in $D=4$ by particular realizations of $\hat{o}(1,5)$ algebra, what illustrates the property that in noncommutative geometry different $D=4$ physical models may be described by various realizations of the same algebraic structure. Finally, in the last Section we propose two new ways of generalizing Yang models: by introducing $\hat o(1,3+2N)$ algebras ($N=1,2\ldots$) we provide internal symmetries $O(N)$ symmetries in Kaluza-Klein extended Yang model, and by replacing the classical $\hat{o}(1,5)$ algebras which describe the algebraic structure of Yang models by $\hat o(1,5)$ quantum groups with suitably chosen nonprimitive coproducts.- 31 July 2024
- Published by Sissa Medialab Srl
- Vol. 463, 247
Open AccessDoubly $\kappa$-deformed Yang models, Born - selfdual $\kappa$-deformed quantum phase spaces and two generalizations of Yang models
Recently it was shown that by using two different realizations of $\hat{o}(1,4)$ Lie algebra one can describe one-parameter standard Snyder model and two-parameter $\kappa$-deformed Snyder model. In this paper, by using the generalized Born duality and Jacobi identities we obtain from the $\kappa$-deformed Snyder model the doubly $\kappa$-deformed Yang model which provides the new class of quantum relativistic phase spaces. These phase spaces contain as subalgebras the $\kappa$-deformed Minkowski space-time as well as quantum $\tilde{\kappa}$-deformed fourmomenta and are depending on five independent parameters. Such a large class of quantum phase spaces can be described in $D=4$ by particular realizations of $\hat{o}(1,5)$ algebra, what illustrates the property that in noncommutative geometry different $D=4$ physical models may be described by various realizations of the same algebraic structure. Finally, in the last Section we propose two new ways of generalizing Yang models: by introducing $\hat o(1,3+2N)$ algebras ($N=1,2\ldots$) we provide internal symmetries $O(N)$ symmetries in Kaluza-Klein extended Yang model, and by replacing the classical $\hat{o}(1,5)$ algebras which describe the algebraic structure of Yang models by $\hat o(1,5)$ quantum groups with suitably chosen nonprimitive coproducts. - Open Access
- 8 November 2023
- Published by Sissa Medialab Srl
- Vol. 436, 327
$\hbar$ -perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
We introduce the perturbative $\hbar $-power series ($\hbar $ - Planck constant) providing the algebraic solutions of $D=4$ quantum Snyder and Yang models which describe relativistic quantum space-times and Lorentz-covariant quantum phase spaces. We argue that if in these series the zero order ($\hbar $-independent) terms are non-vanishing they describe the spontaneous symmetry breaking (SSB) parameters of Lie-algebraic symmetries which characterize the considered models ($D=4$ dS symmetry in Snyder and $D=5$ dS symmetry in Yang cases). The consecutive terms in $\hbar $-power series can be calculated explicitly if we supplement the SSB order parameters (Nambu-Goldstone or NG modes) by dual set of commutative momenta, which together define the canonical tensorial Heisenberg algebra.- 8 November 2023
- Published by Sissa Medialab Srl
- Vol. 436, 327
Open Access$\hbar$ -perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
We introduce the perturbative $\hbar $-power series ($\hbar $ - Planck constant) providing the algebraic solutions of $D=4$ quantum Snyder and Yang models which describe relativistic quantum space-times and Lorentz-covariant quantum phase spaces. We argue that if in these series the zero order ($\hbar $-independent) terms are non-vanishing they describe the spontaneous symmetry breaking (SSB) parameters of Lie-algebraic symmetries which characterize the considered models ($D=4$ dS symmetry in Snyder and $D=5$ dS symmetry in Yang cases). The consecutive terms in $\hbar $-power series can be calculated explicitly if we supplement the SSB order parameters (Nambu-Goldstone or NG modes) by dual set of commutative momenta, which together define the canonical tensorial Heisenberg algebra. - Open Access
$\hbar$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
We introduce the perturbative $\hbar$-power series ($\hbar$ = Planck constant) providing the algebraic solutions of $D=4$ quantum Snyder and Yang models which describe relativistic quantum space-times and Lorentz-covariant quantum phase spaces. We argue that if in these series the zero order ($\hbar $-independent) terms are non-vanishing they describe the spontaneous symmetry breaking (SSB) parameters of Lie-algebraic symmetries which characterize the considered models ($D=4$ dS symmetry in Snyder and $D=5$ dS symmetry in Yang cases). The consecutive terms in $\hbar$-power series can be calculated explicitly if we supplement the SSB order parameters (Nambu-Goldstone or NG modes) by dual set of commutative momenta, which together define the canonical tensorial Heisenberg algebra.Open Access$\hbar$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
We introduce the perturbative $\hbar$-power series ($\hbar$ = Planck constant) providing the algebraic solutions of $D=4$ quantum Snyder and Yang models which describe relativistic quantum space-times and Lorentz-covariant quantum phase spaces. We argue that if in these series the zero order ($\hbar $-independent) terms are non-vanishing they describe the spontaneous symmetry breaking (SSB) parameters of Lie-algebraic symmetries which characterize the considered models ($D=4$ dS symmetry in Snyder and $D=5$ dS symmetry in Yang cases). The consecutive terms in $\hbar$-power series can be calculated explicitly if we supplement the SSB order parameters (Nambu-Goldstone or NG modes) by dual set of commutative momenta, which together define the canonical tensorial Heisenberg algebra. - Open Access
- 23 November 2022
- Published by Sissa Medialab Srl
- Vol. 406, 290
Noncommutative spaces and superspaces from Snyder and Yang type models
The relativistic = 4 Snyder model is formulated in terms of = 4 algebra (4, 1) generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by (4,1) (3,1) coset generators. Analogously, in relativistic = 4 Yang models the quantum-deformed relativistic phase space is described by the algebras of coset generators (5,1) (3,1) or (4,2) (3,1). We extend these algebraic considerations by using respective superalgebras, which provide Lorentz-covariant quantum superspaces (SUSY Snyder model) as well as relativistic quantum phase super spaces (SUSY Yang model).
- 23 November 2022
- Published by Sissa Medialab Srl
- Vol. 406, 290
Open AccessNoncommutative spaces and superspaces from Snyder and Yang type models
The relativistic = 4 Snyder model is formulated in terms of = 4 algebra (4, 1) generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by (4,1) (3,1) coset generators. Analogously, in relativistic = 4 Yang models the quantum-deformed relativistic phase space is described by the algebras of coset generators (5,1) (3,1) or (4,2) (3,1). We extend these algebraic considerations by using respective superalgebras, which provide Lorentz-covariant quantum superspaces (SUSY Snyder model) as well as relativistic quantum phase super spaces (SUSY Yang model).
- Open Access
Internal quark symmetries and colour SU(3) entangled with Z_3-graded Lorentz algebra
In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the $SU(3)$ colour, the $SU(2)$ flavour, and broken $SU(3)$ providing the family triplets. \noindent In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the $SU(3)$ colour algebra is endowed with natural $Z_3$-graded discrete automorphisms, in order to introduce entanglement the $Z_3$-graded version of Lorentz and Poincar\'e algebras with their realizations are considered. The colour multiplets of quarks are described by $12$-component colour Dirac equations, with a $Z_3$-graded triplet of masses (one real and a Lee-Wick complex conjugate pair). We argue that all quarks in the Standard Model can be described by the $72$-component master quark sextet of $12$-component coloured Dirac fields.Open AccessInternal quark symmetries and colour SU(3) entangled with Z_3-graded Lorentz algebra
In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the $SU(3)$ colour, the $SU(2)$ flavour, and broken $SU(3)$ providing the family triplets. \noindent In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the $SU(3)$ colour algebra is endowed with natural $Z_3$-graded discrete automorphisms, in order to introduce entanglement the $Z_3$-graded version of Lorentz and Poincar\'e algebras with their realizations are considered. The colour multiplets of quarks are described by $12$-component colour Dirac equations, with a $Z_3$-graded triplet of masses (one real and a Lee-Wick complex conjugate pair). We argue that all quarks in the Standard Model can be described by the $72$-component master quark sextet of $12$-component coloured Dirac fields. - Open Access
Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras
We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed quantum inhomogeneous conformal Hopf algebras ) and ), where describes complex twistor coordinates and the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of Heisenberg-conformal algebra (HCA) ( is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length , is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in . We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebraOpen AccessPalatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras
We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed quantum inhomogeneous conformal Hopf algebras ) and ), where describes complex twistor coordinates and the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of Heisenberg-conformal algebra (HCA) ( is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length , is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in . We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra - Open Access
Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras
We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed $D=4$ quantum inhomegeneous conformal Hopf algebras $\mathcal{U}_{\theta }(su(2,2)\ltimes T^{4}$) and $\mathcal{U}_{\bar{\theta}}(su(2,2)\ltimes\bar{T}^{4}$), where $T^{4}$ describe complex twistor coordinatesand $\bar{T}^{4}$ the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently we introduce the quantum deformations of $D=4$ Heisenberg-conformal algebra (HCA) $su(2,2)\ltimes H^{4,4}_\hslash$ ($H^{4,4}_\hslash=\bar{T}^4 \ltimes_\hslash T_4$ is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length $\lambda_p$ will be called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We shall describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and by the quantization map in $H_\hslash^{4,4}$. We introduce as well generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra $\mathcal{U}_\theta(su(2,2)\ltimes T^4).$Open AccessPalatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras
We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed $D=4$ quantum inhomegeneous conformal Hopf algebras $\mathcal{U}_{\theta }(su(2,2)\ltimes T^{4}$) and $\mathcal{U}_{\bar{\theta}}(su(2,2)\ltimes\bar{T}^{4}$), where $T^{4}$ describe complex twistor coordinatesand $\bar{T}^{4}$ the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently we introduce the quantum deformations of $D=4$ Heisenberg-conformal algebra (HCA) $su(2,2)\ltimes H^{4,4}_\hslash$ ($H^{4,4}_\hslash=\bar{T}^4 \ltimes_\hslash T_4$ is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length $\lambda_p$ will be called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We shall describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and by the quantization map in $H_\hslash^{4,4}$. We introduce as well generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra $\mathcal{U}_\theta(su(2,2)\ltimes T^4).$ - Open Access
- 15 September 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (9) , 1-42
Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits
Following the recently obtained complete classification of quantum-deformed $$ \mathfrak{o} $$ (4), $$ \mathfrak{o} $$ (1, 3) and $$ \mathfrak{o} $$ (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail.- 15 September 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (9) , 1-42
Open AccessQuantum D = 3 Euclidean and Poincaré symmetries from contraction limits
Following the recently obtained complete classification of quantum-deformed $$ \mathfrak{o} $$ (4), $$ \mathfrak{o} $$ (1, 3) and $$ \mathfrak{o} $$ (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail. - Open Access
- 1 December 2019
- Published by IOP Publishing in Journal of Physics: Conference Series
- Vol. 1416 (1) , 012016
Towards a Z3-graded approach to quarks’ symmetries
Colour SU(3) group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, SU(2) and U(1), it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour SU(3) symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values 1/3 and 2/3 suggest that the cyclic group Z 3 may play a crucial role in quark field dynamics. In this paper we consequently apply the Z 3 symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured 12-component spinors is introduced and its properties are discussed. Imposing Z 3-graded Lorentz and Poincaré covariance leads to enlargement of quark fields multiplets and incorporates additional Z 2 × Z 3 symmetry which leads to the appearance of three generations (families) of distinct quark doublets.
- 1 December 2019
- Published by IOP Publishing in Journal of Physics: Conference Series
- Vol. 1416 (1) , 012016
Open AccessTowards a Z3-graded approach to quarks’ symmetries
Colour SU(3) group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, SU(2) and U(1), it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour SU(3) symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values 1/3 and 2/3 suggest that the cyclic group Z 3 may play a crucial role in quark field dynamics. In this paper we consequently apply the Z 3 symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured 12-component spinors is introduced and its properties are discussed. Imposing Z 3-graded Lorentz and Poincaré covariance leads to enlargement of quark fields multiplets and incorporates additional Z 2 × Z 3 symmetry which leads to the appearance of three generations (families) of distinct quark doublets.
- Open Access
Towards a $Z_3$-graded approach to quarks' symmetries
Colour $SU(3)$ group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, $SU(2)$ and $U(1)$, it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour$SU(3)$ symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values $1/3$ and $2/3$ suggest that the cyclic group $Z_3$ may play a crucial role in quark field dynamics. In this paper we consequently apply the $Z_3$ symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured $12$-component spinors is introduced and its properties are discussed. Imposing $Z_3$-graded Lorentz and Poincar\'e covariance leads to enlargement of quark fields multiplets and incorporates additional $Z_2 \times Z_3$ symmetry which leads to the appearance of three generations (families) of distinct quark doublets.Open AccessTowards a $Z_3$-graded approach to quarks' symmetries
Colour $SU(3)$ group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, $SU(2)$ and $U(1)$, it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour$SU(3)$ symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values $1/3$ and $2/3$ suggest that the cyclic group $Z_3$ may play a crucial role in quark field dynamics. In this paper we consequently apply the $Z_3$ symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured $12$-component spinors is introduced and its properties are discussed. Imposing $Z_3$-graded Lorentz and Poincar\'e covariance leads to enlargement of quark fields multiplets and incorporates additional $Z_2 \times Z_3$ symmetry which leads to the appearance of three generations (families) of distinct quark doublets.