Jerzy Lukierski - Academia.edu (original) (raw)

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Papers by Jerzy Lukierski

We extend the Shirafuji model for massless particles with primary spacetime coordinates and compo... more We extend the Shirafuji model for massless particles with primary spacetime coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the spacetime four-vector, four scalars describing spin and charge degrees of freedom as well as a pair of Weyl spinors. The geometric description proposed in this paper provides an intermediate step between the free purely twistorial model in two-twistor space in which both spacetime and four-momenta vectors are composite, and the standard particle model, where both spacetime and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wavefunctions describing relativistic particles with mass, spin and electric charge. The spacetime coordinates in the model are not commutative; this leads to a wavefunction that depends only on one covariant projection of the spacetime four-vector defining plane wave solutions.

Physics Letters B, 2014

ABSTRACT

Journal of High Energy Physics, 2013

ABSTRACT

Il Nuovo Cimento A, 1970

The generalization of Thirring's formulation of the Zachariasen model in the presence of a CDD po... more The generalization of Thirring's formulation of the Zachariasen model in the presence of a CDD pole is given. The local field operator, describing an interacting CDD particle, is introduced. It is shown that the CDD pole can be interpreted as a particle only if the mass renormalization in the Zachariasen model is finite. OF THE ZACHARIASEN MODEL WITtt A CDD POLE 419

Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy PlebańSki - Proceedings of 2002 International Conference, 2006

We describe the generalized κ-deformations of D = 4 relativistic symmetries with finite masslike ... more We describe the generalized κ-deformations of D = 4 relativistic symmetries with finite masslike deformation parameter κ and an arbitrary direction in κ-deformed Minkowski space being noncommutative. The corresponding bicovariant differential calculi on κdeformed Minkowski spaces are considered. Two distinguished cases are discussed: 5D noncommutative differential calculus (κ-deformation in time-like or space-like direction), and 4D noncommutative differential calculus having the classical dimension (noncommutative κ-deformation in light-like direction). We introduce also left and right vector fields acting on functions of noncommutative Minkowski coordinates, and describe the noncommutative differential realizations of κ-deformed Poincaré algebra. The κ-deformed Klein-Gordon field on noncommutative Minkowski space with noncommutative time (standard κ-deformation) as well as noncommutative null line (light-like κ-deformation) are discussed. Following our earlier proposal (see [1, 2]) we introduce an equivalent framework replacing the local noncommutative field theory by the nonlocal commutative description with suitable nonlocal star product multiplication rules. The modification of Pauli-Jordan commutator function is described and the κ-dependence of its light-cone behaviour in coordinate space is explicitely given. The problem with the κ-deformed energy-momentum conservation law is recalled. * Supported by KBN grant 5P03B05620

Nuclear Physics B - Proceedings Supplements, 2001

We describe the extension of the Wigner's infinite-dimensional unitary representations of Poincar... more We describe the extension of the Wigner's infinite-dimensional unitary representations of Poincar@ group to the case of n-deformed Poincar@ group. We show that the corresponding coordinate wave functions on noncommutative space-time are described by free field equations on n-deformed Minkowski space. The cases of Klein-Gordon, Dirac, Proca and Maxwell fields are considered. Finally some aspects of second quantization are also discussed.

After recalling the notion of Galilean conformal (GC) algebra we introduce in arbitrary space dim... more After recalling the notion of Galilean conformal (GC) algebra we introduce in arbitrary space dimension d the nonrelativistic (Galilean) twistors as the spinorial realization of SO(2,1){\oplus}SO(d). The GC-covariant quantization of Galilean twistors is presented. We consider for d=3 the general spinorial matrix realizations of GC algebra, which are further promoted to quantum-mechanical operator representations, expressed as bilinears in quantized Galilean

We describe the generalized kappa-deformations of D=4 relativistic symmetries with finite masslik... more We describe the generalized kappa-deformations of D=4 relativistic symmetries with finite masslike deformation parameter kappa and an arbitrary direction in kappa-deformed Minkowski space being noncommutative. The corresponding bicovariant differential calculi on kappa-deformed Minkowski spaces are considered. Two distinguished cases are discussed: 5D noncommutative differential calculus (kappa-deformation in time-like or space-like direction), and 4D noncommutative differential calculus having the classical dimension

Physical Review D, 2007

We introduce the D 4 twistorial tensionfull bosonic string by considering the canonical twistoria... more We introduce the D 4 twistorial tensionfull bosonic string by considering the canonical twistorial 2form in two-twistor space. We demonstrate its equivalence to two bosonic string models: due to Siegel (with covariant world-sheet vectorial string momenta P m ; ) and the one with tensorial string momenta P ; . We show how to obtain in mixed spacetime-twistor formulation the Soroka-Sorokin-Tkach-Volkov (SSTV) string model and subsequently by harmonic gauge fixing the Bandos-Zheltukhin (BZ) model, with constrained spinorial coordinates.

Physical Review D, 2007

We describe D=4 twistorial membrane in terms of two twistorial three-dimensional world volume fie... more We describe D=4 twistorial membrane in terms of two twistorial three-dimensional world volume fields. We start with the D-dimensional p-brane generalizations of two phase space string formulations: one with p+1 vectorial momenta, and the second with tensorial momenta of (p+1)-th rank. Further, we consider the tensionful membrane case in D=4. By using the membrane generalization of the Cartan-Penrose formula, we

Physical Review D, 2011

ABSTRACT We apply the nonlinear realizations method for constructing new Galilean conformal mecha... more ABSTRACT We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a non-relativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension D=d+1 (no central charges), as well as in the special dimension D=2+1 with one "exotic" central charge. We obtain new classical mechanics models which extend the standard (D=0+1) conformal mechanics in the presence of d non-vanishing space dimensions.

Noncommutative Structures in Mathematics and Physics, 2001

We review shortly present status of quantum deformations of Poincaré and conformal super symmetri... more We review shortly present status of quantum deformations of Poincaré and conformal super symmetries. After recalling the κ-deformation of D=4 Poincaré supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral vertices in momentum space the integration formula over κ-deformed chiral superspace is proposed.

We extend the Shirafuji model for massless particles with primary spacetime coordinates and compo... more We extend the Shirafuji model for massless particles with primary spacetime coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the spacetime four-vector, four scalars describing spin and charge degrees of freedom as well as a pair of Weyl spinors. The geometric description proposed in this paper provides an intermediate step between the free purely twistorial model in two-twistor space in which both spacetime and four-momenta vectors are composite, and the standard particle model, where both spacetime and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wavefunctions describing relativistic particles with mass, spin and electric charge. The spacetime coordinates in the model are not commutative; this leads to a wavefunction that depends only on one covariant projection of the spacetime four-vector defining plane wave solutions.

Physics Letters B, 2014

ABSTRACT

Journal of High Energy Physics, 2013

ABSTRACT

Il Nuovo Cimento A, 1970

The generalization of Thirring's formulation of the Zachariasen model in the presence of a CDD po... more The generalization of Thirring's formulation of the Zachariasen model in the presence of a CDD pole is given. The local field operator, describing an interacting CDD particle, is introduced. It is shown that the CDD pole can be interpreted as a particle only if the mass renormalization in the Zachariasen model is finite. OF THE ZACHARIASEN MODEL WITtt A CDD POLE 419

Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy PlebańSki - Proceedings of 2002 International Conference, 2006

We describe the generalized κ-deformations of D = 4 relativistic symmetries with finite masslike ... more We describe the generalized κ-deformations of D = 4 relativistic symmetries with finite masslike deformation parameter κ and an arbitrary direction in κ-deformed Minkowski space being noncommutative. The corresponding bicovariant differential calculi on κdeformed Minkowski spaces are considered. Two distinguished cases are discussed: 5D noncommutative differential calculus (κ-deformation in time-like or space-like direction), and 4D noncommutative differential calculus having the classical dimension (noncommutative κ-deformation in light-like direction). We introduce also left and right vector fields acting on functions of noncommutative Minkowski coordinates, and describe the noncommutative differential realizations of κ-deformed Poincaré algebra. The κ-deformed Klein-Gordon field on noncommutative Minkowski space with noncommutative time (standard κ-deformation) as well as noncommutative null line (light-like κ-deformation) are discussed. Following our earlier proposal (see [1, 2]) we introduce an equivalent framework replacing the local noncommutative field theory by the nonlocal commutative description with suitable nonlocal star product multiplication rules. The modification of Pauli-Jordan commutator function is described and the κ-dependence of its light-cone behaviour in coordinate space is explicitely given. The problem with the κ-deformed energy-momentum conservation law is recalled. * Supported by KBN grant 5P03B05620

Nuclear Physics B - Proceedings Supplements, 2001

We describe the extension of the Wigner's infinite-dimensional unitary representations of Poincar... more We describe the extension of the Wigner's infinite-dimensional unitary representations of Poincar@ group to the case of n-deformed Poincar@ group. We show that the corresponding coordinate wave functions on noncommutative space-time are described by free field equations on n-deformed Minkowski space. The cases of Klein-Gordon, Dirac, Proca and Maxwell fields are considered. Finally some aspects of second quantization are also discussed.

After recalling the notion of Galilean conformal (GC) algebra we introduce in arbitrary space dim... more After recalling the notion of Galilean conformal (GC) algebra we introduce in arbitrary space dimension d the nonrelativistic (Galilean) twistors as the spinorial realization of SO(2,1){\oplus}SO(d). The GC-covariant quantization of Galilean twistors is presented. We consider for d=3 the general spinorial matrix realizations of GC algebra, which are further promoted to quantum-mechanical operator representations, expressed as bilinears in quantized Galilean

We describe the generalized kappa-deformations of D=4 relativistic symmetries with finite masslik... more We describe the generalized kappa-deformations of D=4 relativistic symmetries with finite masslike deformation parameter kappa and an arbitrary direction in kappa-deformed Minkowski space being noncommutative. The corresponding bicovariant differential calculi on kappa-deformed Minkowski spaces are considered. Two distinguished cases are discussed: 5D noncommutative differential calculus (kappa-deformation in time-like or space-like direction), and 4D noncommutative differential calculus having the classical dimension

Physical Review D, 2007

We introduce the D 4 twistorial tensionfull bosonic string by considering the canonical twistoria... more We introduce the D 4 twistorial tensionfull bosonic string by considering the canonical twistorial 2form in two-twistor space. We demonstrate its equivalence to two bosonic string models: due to Siegel (with covariant world-sheet vectorial string momenta P m ; ) and the one with tensorial string momenta P ; . We show how to obtain in mixed spacetime-twistor formulation the Soroka-Sorokin-Tkach-Volkov (SSTV) string model and subsequently by harmonic gauge fixing the Bandos-Zheltukhin (BZ) model, with constrained spinorial coordinates.

Physical Review D, 2007

We describe D=4 twistorial membrane in terms of two twistorial three-dimensional world volume fie... more We describe D=4 twistorial membrane in terms of two twistorial three-dimensional world volume fields. We start with the D-dimensional p-brane generalizations of two phase space string formulations: one with p+1 vectorial momenta, and the second with tensorial momenta of (p+1)-th rank. Further, we consider the tensionful membrane case in D=4. By using the membrane generalization of the Cartan-Penrose formula, we

Physical Review D, 2011

ABSTRACT We apply the nonlinear realizations method for constructing new Galilean conformal mecha... more ABSTRACT We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a non-relativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension D=d+1 (no central charges), as well as in the special dimension D=2+1 with one "exotic" central charge. We obtain new classical mechanics models which extend the standard (D=0+1) conformal mechanics in the presence of d non-vanishing space dimensions.

Noncommutative Structures in Mathematics and Physics, 2001

We review shortly present status of quantum deformations of Poincaré and conformal super symmetri... more We review shortly present status of quantum deformations of Poincaré and conformal super symmetries. After recalling the κ-deformation of D=4 Poincaré supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral vertices in momentum space the integration formula over κ-deformed chiral superspace is proposed.