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-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
Jerzy Lukierski, Anna Pachoł
We introduce the perturbative -power series ( = Planck constant) providing the algebraic solutions of quantum Snyder and Yang models which describe relativistic…
Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
Jerzy Lukierski, Stjepan Meljanac, Salvatore Mignemi +1
We propose -expansions as perturbative solutions of quantum extended Snyder and Yang models, with -independent classical zero-th order terms responsible for the spont…
Generalized quantum phase spaces for the -deformed extended Snyder model
Jerzy Lukierski, Stjepan Meljanac, Salvatore Mignemi +1
We describe, in an algebraic way, the -deformed extended Snyder models, that depend on three parameters and , which in a suitable algebra basis are described by the de…
Noncommutative spaces and superspaces from Snyder and Yang type models
Jerzy Lukierski, Mariusz Woronowicz
The relativistic Snyder model is formulated in terms of algebra generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by $\…
Spinorial Snyder and Yang Models From Superalgebras And Noncommutative Quantum Superspaces
Jerzy Lukierski, Mariusz Woronowicz
The relativistic Lorentz-covariant quantum space-times obtained by Snyder can be described by the coset generators of (anti) de-Sitter algebras. Similarly, the Lorentz-covariant qu…
Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras
Jerzy Lukierski
We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed quantum inhomegeneous conformal Hopf algebras $\mathcal…
Internal quark symmetries and colour SU(3) entangled with Z_3-graded Lorentz algebra
Richard Kerner, Jerzy Lukierski
In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the colour, the flavour, a…
Towards a -graded approach to quarks' symmetries
Richard Kerner, Jerzy Lukierski
Colour group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, …
Quantum Euclidean and Poincaré symmetries from contraction limits
Jerzy Kowalski-Glikman, Jerzy Lukierski, Tomasz Trześniewski
Following the recently obtained complete classification of quantum-deformed , and algebras, characterized by classical -…
Two -deformed covariant relativistic quantum phase spaces as Poincare-Hopf algebroids
Jerzy Lukierski, Mariusz Woronowicz
We consider two quantum phase spaces which can be described by two Hopf algebroids linked with the well-known -deformed Poincare-Hopf algebra . The first…
Z_3 - graded colour Dirac equations for quarks, confinement and generalized Lorentz symmetries
Richard Kerner, Jerzy Lukierski
We propose a modification of standard QCD description of the colour triplet of quarks describing quark fields endowed with colour degree of freedom by introducing a 12-component co…
Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
Jerzy Lukierski, Stjepan Meljanac, Mariusz Woronowicz
We consider the generalized (10+10)-dimensional D=4 quantum phase spaces containing translational and Lorentz spin sectors associated with the dual pair of twist-quantized Poincare…
From Galilean superparticle to three-dimensional non-relativistic superfields
Sergey Fedoruk, Evgeny Ivanov, Jerzy Lukierski
We consider the general Galilean superalgebra with arbitrary central charges and study its dynamical realizations. Using the nonlinear realization te…
Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
Jerzy Lukierski, Daniel Meljanac, Stjepan Meljanac +2
We consider new Abelian twists of Poincare algebra describing non-symmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski space…
Basic quantizations of Euclidean, Lorentz, Kleinian and quaternionic symmetries
A. Borowiec, J. Lukierski, V. N. Tolstoy
We construct firstly the complete list of five quantum deformations of complex homogeneous orthogonal Lie algebra $\mathfrak{o}(4;\mathbb{C})\cong \mathfrak{o}(3;\mathbb{C})\…
Quantizations of D=3 Lorentz symmetry
J. Lukierski, V. N. Tolstoy
Using the isomorphism we develop a new simple algebraic technique for complete classification of quantum deformations…
Kappa-Deformations: Historical Developments and Recent Results
Jerzy Lukierski
I shall recall in historical perspective some results from nineties and show further how -deformed symmetries and -Minkowski space inspired DSR (Doubly of Deformed Special Re…
Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincare / super-Euclidean r-matrices
Andrzej Borowiec, Jerzy Lukierski, Valerij N. Tolstoy
We provide the classification of real forms of complex D=4 Euclidean algebra as well as (…
Yang-Baxter sigma models and Lax pairs arising from -Poincaré -matrices
Andrzej Borowiec, Hideki Kyono, Jerzy Lukierski +2
We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical -matrices associated with -deformations of the Poincaré algebra. These classica…
Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
Jerzy Lukierski, Zoran Skoda, Mariusz Woronowicz
We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase space as given by Heisenberg double \mathcal{H} of D=4 kappa-deformed Poincare-Hopf algebra H. The stan…
Quantum Gravity models - brief conceptual summary
Jerzy Lukierski
After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical c…
Massive twistor particle with spin generated by Souriau-Wess-Zumino term and its quantization
Sergey Fedoruk, Jerzy Lukierski
We present new model of D=4 relativistic massive particle with spin and we describe its quantization. The model is obtained by an extension of standard relativistic phase space des…
Noncommutative Space-time from Quantized Twistors
Jerzy Lukierski, Mariusz Woronowicz
We consider the relativistic phase space coordinates (x_μ,p_μ) as composite, described by functions of the primary pair of twistor coordinates. It appears that if twistor coordinat…
Maxwell group and HS field theory
Sergey Fedoruk, Jerzy Lukierski
We consider the master fields for HS multiplets defined on 10-dimensional tensorial extension \tilde{\cal M} of D=4 space-time described as a coset \tilde{\cal M}={\cal M}/Sl(2;C)…