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.
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
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
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.
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
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
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.
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Papers by Jerzy Lukierski