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Jerzy Lukierski

Publications and source records attributed to Jerzy Lukierski.

90 records · Page 5Linked to original sources
arXiv2001

From noncommutative space-time to quantum relativistic symmetries with fundamental mass parameter

We consider the simplest class of Lie-algebraic deformations of space-time algebra, with the selection of $κ$-deformations as providing quantum deformation of relativistic framework. We recall that the $κ$-deformation along any direction in Minkowski space can be obtained. Some problems of the formalism of $κ$-deformations will be considered. We shall comment on the conformal extension of light-like $κ$-deformation as well as on the applications to astrophysical problems.

hep-th↗
arXiv2001

An action for supergravity interacting with super-p-brane sources

We describe the coupled system of supergravity and a superbrane source by the sum of the group manifold action for D--dimensional supergravity and the action for a super--$p$--brane. We derive the generalized Einstein equation with the source and discuss the local fermionic symmetries of the coupled action. Our scheme could be especially relevant in $D=11, 10$, in which the superfield actions for supergravity are not known.

hep-th↗
arXiv2001

BPS states in M-theory and twistorial constituents

We provide a complete algebraic description of BPS states in M-theory in terms of primary constituents that we call BPS preons. We argue that any BPS state preserving $k$ of the 32 supersymmetries is a composite of (32-k) BPS preons. In particular, the BPS states corresponding to the basic M2 and M5 branes are composed of 16 BPS preons. By extending the M-algebra to a generalized D=11 conformal superalgebra $osp(1|64)$ we relate the BPS preons with its fundamental representation, the D=11 supertwistors.

hep-th↗
arXiv1999

The OSp(1|4) Superparticle and Exotic BPS States

We discuss the dynamics of a superparticle in a superspace whose isometry is generated by the superalgebra OSp(1|4) or its central-charge contraction. Extra coordinates of the superspace associated with tensorial central charges are shown to describe spin degrees of freedom of the superparticle, so quantum states form an infinite tower of (half)-integer helicities. A peculiar feature of the model is that it admits BPS states which preserve 3/4 of target-space supersymmetries.

hep-th↗
arXiv1999

Generalized Superconformal Symmetries and Supertwistor Dynamics

We show that in the supersymmetry framework described by a Poincaré superalgebra with tensorial central charges the role of generalized superconformal symmetry which contains all these central charges is played by $OSp(1|2^{k})$, where k=3 for D=4. Following [1,2] we describe the free supertwistor model for $OSp(1|8)$. It appears that in such a scheme the tensorial central charges satisfy additional relations and the model describes the tower of supersymmetric massless states with an arbitrary (integer and half--integer) helicity spectrum.

hep-th↗
arXiv1999

OSp supergroup manifolds, superparticles and supertwistors

We construct simple twistor-like actions describing superparticles propagating on a coset superspace OSp(1|4)/SO(1,3) (containing the D=4 anti-de-Sitter space as a bosonic subspace), on a supergroup manifold OSp(1|4) and, generically, on OSp(1|2n). Making two different contractions of the superparticle model on the OSp(1|4) supermanifold we get massless superparticles in Minkowski superspace without and with tensorial central charges. Using a suitable parametrization of OSp(1|2n) we obtain even Sp(2n)-valued Cartan forms which are quadratic in Grassmann coordinates of OSp(1|2n). This result may simplify the structure of brane actions in super-AdS backgrounds. For instance, the twistor-like actions constructed with the use of the even OSp(1|2n) Cartan forms as supervielbeins are quadratic in fermionic variables. We also show that the free bosonic twistor particle action describes massless particles propagating in arbitrary space-times with a conformally flat metric, in particular, in Minkowski space and AdS space. Applications of these results to the theory of higher spin fields and to superbranes in AdS superbackgrounds are mentioned.

hep-th↗
arXiv1999

Superparticle Models with Tensorial Central Charges

A generalization of the Ferber-Shirafuji formulation of superparticle mechanics is considered. The generalized model describes the dynamics of a superparticle in a superspace extended by tensorial central charge coordinates and commuting twistor-like spinor variables. The D=4 model contains a continuous real parameter $a\geq 0$ and at a=0 reduces to the SU(2,2|1) supertwistor Ferber-Shirafuji model, while at a=1 one gets an OSp(1|8) supertwistor model of ref. [1] (hep-th/9811022) which describes BPS states with all but one unbroken target space supersymmetries. When 0 1 the supertwistor group becomes OSp(1,1|8). We quantize the model and find that its quantum spectrum consists of massless states of an arbitrary (half)integer helicity. The independent discrete central charge coordinate describes the helicity spectrum. We also outline the generalization of the a=1 model to higher space-time dimensions and demonstrate that in D=3,4,6 and 10, where the quantum states are massless, the extra degrees of freedom (with respect to those of the standard superparticle) parametrize compact manifolds. These compact manifolds can be associated with higher-dimensional helicity states. In particular, in D=10 the additional ``helicity'' manifold is isomorphic to the seven-sphere.

hep-th↗
arXiv1999

Distance Measurement and $κ$-Deformed Propagation of Light and Heavy Probes

We investigate the implications for the measurability of distances of a covariant dimensionful ``$κ$'' deformation of D=4 relativistic symmetries, with quantum time coordinate and modified Heisenberg algebra. We show that the structure of the deformed mass-shell condition has significant implications for measurement procedures relying on light probes, whereas in the case of heavy probes the most sizeable effect is due to the nontrivial commutation relation between three-momenta and quantum time coordinate. We argue that these findings might indicate that $κ$-Poincaré symmetries capture some aspects of the physics of the Quantum-Gravity vacuum.

gr-qc↗
arXiv1999

Tensorial Central Charges and New Superparticle Models with Fundamental Spinor Coordinates

We consider firstly simple D=4 superalgebra with six real tensorial central charges $Z_{μν}$, and discuss its possible realizations in massive and massless cases. Massless case is dynamically realized by generalized Ferber-Shirafuji (FS) model with fundamental bosonic spinor coordinates. The Lorentz invariance is not broken due to the realization of central charges generators in terms of bosonic spinors. The model contains four fermionic coordinates and possesses three kappa-symmetries thus providing the BPS configuration preserving 3/4 of the target space supersymmetries. We show that the physical degrees of freedom (8 real bosonic and 1 real Grassmann variable) of our model can be described by OSp(8|1) supertwistor. The relation with recent superparticle model by Rudychev and Sezgin is pointed out. Finally we propose a higher dimensional generalization of our model with one real fundamental bosonic spinor. D=10 model describes massless superparticle with composite tensorial central charges and in D=11 we obtain 0-superbrane model with nonvanishing mass which is generated dynamically.

hep-th↗
arXiv1998

New Superparticle Models Outside the HLS Supersymmetry Scheme

We consider the superparticle models invariant under the supersymmetries with tensorial central charges, which were not included in D=4 Haag-Lopuszanski-Sohnius (HLS) supersymmetry scheme. We present firstly a generalization of D=4 Ferber-Shirafuji (FS) model with fundamental bosonic spinors and tensorial central charge coordinates. The model contains four fermionic coordinates and possesses three kappa- symmetries thus providing the BPS configuration preserving 3/4 of the target space supersymmetries. We show that the physical degrees of freedom (8 real bosonic and 1 real Grassmann variable) of our model can be described by OSp(8|1) supertwistor. Then we propose a higher dimensional generalization of our model with one real fundamental bosonic spinor. D=10 model describes massless superparticle with composite tensorial central charges and in D=11 we obtain 0-superbrane model with nonvanishing mass which is generated dynamically. The introduction of D=11 Lorentz harmonics provides the possibility to construct massless D=11 superparticle model which can be formulated in a way preserving 1/2, 17/32, 18/32,..., 31/32 supersymmetries. In a special case we obtain the twistor-like formulation of the usual massless D=11 superparticle proposed recently by Bergshoeff and Townsend.

hep-th↗
arXiv1997

kappa-Deformed Covariant Phase Space and Quantum-Gravity Uncertainty Relations

We describe the deformed covariant phase space corresponding to the so-called kappa-deformation of D=4 relativistic symmetries, with quantum ``time'' coordinate and Heisenberg algebra obtained according to the Heisenberg double construction. The associated modified uncertainty relations are analyzed, and in particular it is shown that these relations are consistent with independent estimates of quantum-gravity limitations on the measurability of space-time distances.

hep-th↗
arXiv1996

Quantum Deformations of Space-Time Symmetries and Interactions

We discuss quantum deformations of Lie algebra as described by the noncoassociative modification of its coalgebra structure. We consider for simplicity the quantum $D=1$ Galilei algebra with four generators: energy $H$, boost $B$, momentum $P$ and central generator $M$ (mass generator). We describe the nonprimitive coproducts for $H$ and $B$ and show that their noncocommutative and noncoassociative structure is determined by the two-body interaction terms. Further we consider the case of physical Galilei symmetry in three dimensions. Finally we discuss the noninteraction theorem for manifestly covariant two-body systems in the framework of quantum deformations of $D=4$ \poin algebra and a possible way out.

hep-th↗
arXiv1995

Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters

We consider new class of classical r-matrices for D=3 and D=4 conformal Lie algebras. These r-matrices do satisfy the classical Yang-Baxter equation and as two-tensors belong to the tensor product of Borel subalgebra. In such a way we generalize the lowest order of known nonstandard quantum deformation of sl(2) to the Lie algebras sp(4) = so(5) and sl(4) = so(6). As an exercise we interpret nonstandard deformation of sl(2) as describing quantum D=1 conformal algebra with fundamental mass parameter. Further we describe the D=3 and D=4 conformal bialgebras with deformation parameters equal to the inverse of fundamental masses. It appears that for D=4 the deformation of the Poincare algebra sector coincides with "null plane" quantum Poincare algebra.

q-alg↗
arXiv1995

kappa-deformed realisation of D=4 conformal algebra

We describe the generators of kappa-conformal transformations, leaving invariant the kappa-deformed d'Alembert equation. In such a way one obtains the conformal extension of the off-shell spin zero realization of kappa-deformed Poincare algebra. Finally the algebraic structure of kappa-deformed conformal algebra is discussed.

hep-th↗
arXiv1993

Twisted Classical Poincaré Algebras

We consider the twisting of Hopf structure for classical enveloping algebra $U(\hat{g})$, where $\hat{g}$ is the inhomogenous rotations algebra, with explicite formulae given for $D=4$ Poincaré algebra $(\hat{g}={\cal P}_4).$ The comultiplications of twisted $U^F({\cal P}_4)$ are obtained by conjugating primitive classical coproducts by $F\in U(\hat{c})\otimes U(\hat{c}),$ where $\hat{c}$ denotes any Abelian subalgebra of ${\cal P}_4$, and the universal $R-$matrices for $U^F({\cal P}_4)$ are triangular. As an example we show that the quantum deformation of Poincaré algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincaré algebra. The interpretation of twisted Poincaré algebra as describing relativistic symmetries with clustered 2-particle states is proposed.

hep-th↗
arXiv1993

Quantum $κ$-Poincare in Any Dimensions

The $κ$-deformation of the D-dimensional Poincaré algebra $(D\geq 2)$ with any signature is given. Further the quadratic Poisson brackets, determined by the classical $r$-matrix are calculated, and the quantum Poincaré group "with noncommuting parameters" is obtained.

hep-th↗