arXiv subjects

Jerzy Lukierski

Publications and source records attributed to Jerzy Lukierski.

At least 73 records · Page 4Linked to original sources

arXiv2007

Twistorial and space-time descriptions of D=4 string models

We derive twistorial tensionful bosonic string action by considering on the world sheet the canonical twistorial 2-form in two-twistor space. We demonstrate the equivalence of or model to two known momentum formulations of D=4 bosonic string, with covariant worldsheet vectorial string momenta $P_μ^m(τ,σ)$ and the one with tensorial string momenta $P_{[μν]}(τ,σ)$. All considered here string actions, in twistorial and mixed spinor-spacetime formulations, are classically equivalent to the Nambu-Goto action.

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arXiv2007

Twistorial versus space--time formulations: unification of various string models

We introduce the D=4 twistorial tensionfull bosonic string by considering the canonical twistorial 2--form in two--twistor space. We demonstrate its equivalence to two bosonic string models: due to Siegel (with covariant worldsheet vectorial string momenta $P_μ^{m}(τ,σ)$) and the one with tensorial string momenta $P_{[μν]}(τ,σ)$. We show how to obtain in mixed space-time--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.

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arXiv2006

Quantum $κ$-deformations of D=4 relativistic supersymmetries

We describe the quantum $κ$-deformation of super-Poincaré algebra, with fundamental mass-like deformation parameter $κ$. We shall describe the result in graded bicrossproduct basis, with classical Lorentz superalgebra sector which includes half of the supercharges.

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arXiv2006

Massive relativistic particle model with spin from free two-twistor dynamics and its quantization

We consider a relativistic particle model in an enlarged relativistic phase space M^{18} = (X_μ, P_μ, η_α, \oeta_\dalpha, σ_α, \osigma_\dalpha, e, ϕ), which is derived from the free two-twistor dynamics. The spin sector variables (η_α, \oeta_\dalpha, σ_α,\ osigma_\dalpha) satisfy two second class constraints and account for the relativistic spin structure, and the pair (e,ϕ) describes the electric charge sector. After introducing the Liouville one-form on M^{18}, derived by a non-linear transformation of the canonical Liouville one-form on the two-twistor space, we analyze the dynamics described by the first and second class constraints. We use a composite orthogonal basis in four-momentum space to obtain the scalars defining the invariant spin projections. The first-quantized theory provides a consistent set of wave equations, determining the mass, spin, invariant spin projection and electric charge of the relativistic particle. The wavefunction provides a generating functional for free, massive higher spin fields.

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arXiv2006

Quantum Deformations of Einstein's Relativistic Symmetries

We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory - the Poincaré symmetries. The most complete way of introducing the modifications is via the noncocommutative Hopf-algebraic structure describing quantum symmetries. Two types of quantum relativistic symmetries are described, one with constant commutator of quantum Minkowski space coordinates ($θ_{μν}$-deformation) and second with Lie-algebraic structure of quantum space-time, introducing so-called $κ$-deformation. The third fundamental constant of Nature - fundamental mass $κ$ or length $λ$ - appears naturally in proposed quantum relativistic symmetry scheme. The deformed Minkowski space is described as the representation space (Hopf-module) of deformed Poincaré algebra. Some possible perspectives of quantum-deformed relativistic symmetries will be outlined.

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arXiv2005

Higher Spin Particles with Bosonic Counterpart of Supersymmetry

We propose the relativistic point particle models invariant under the bosonic counterpart of SUSY. The particles move along the world lines in four dimensional Minkowski space extended by $N$ commuting Weyl spinors. The models provide after first quantization the non--Grassmann counterpart of chiral superfields, satisfying Klein--Gordon equation. Free higher spin fields obtained by expansions of such chiral superfields satisfy the N=2 Bargman--Wigner equations in massive case and Fierz--Pauli equations in massless case.

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arXiv2005

Higher Spins from Nonlinear Realizations of $OSp(1|8)$

We exhibit surprising relations between higher spin theory and nonlinear realizations of the supergroup $OSp(1|8)$, a minimal superconformal extension of N=1, 4D supersymmetry with tensorial charges. We construct a realization of $OSp(1|8)$ on the coset supermanifold $OSp(1|8)/SL(4,R)$ which involves the tensorial superspace $R^{(10|4)}$ and Goldstone superfields given on it. The covariant superfield equation encompassing the component ones for all integer and half-integer massless higher spins amounts to the vanishing of covariant spinor derivatives of the suitable Goldstone superfields, and, via Maurer-Cartan equations, to the vanishing of $SL(4,R)$ supercurvature in odd directions of $R^{(10|4)}$. Aiming at higher spin extension of the Ogievetsky-Sokatchev formulation of N=1 supergravity, we generalize the notion of N=1 chirality and construct first examples of invariant superfield actions involving a non-trivial interaction. Some other potential implications of $OSp(1|8)$ in the proposed setting are briefly outlined.

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arXiv2004

The symmetry algebras of Euclidean M-theory

We study the Euclidean supersymmetric D=11 M-algebras. We consider two such D=11 superalgebras: the first one is N=(1,1) self-conjugate complex-Hermitean, with 32 complex supercharges and 1024 real bosonic charges, the second is N=(1,0) complex-holomorphic, with 32 complex supercharges and 528 bosonic charges, which can be obtained by analytic continuation of known Minkowski M-algebra. Due to the Bott's periodicity, we study at first the generic D=3 Euclidean supersymmetry case. The role of complex and quaternionic structures for D=3 and D=11 Euclidean supersymmetry is elucidated. We show that the additional 1024-528=496 Euclidean tensorial central charges are related with the quaternionic structure of Euclidean D=11 supercharges, which in complex notation satisfy SU(2) pseudo-Majorana condition. We consider also the corresponding Osterwalder-Schrader conjugations as implying for N=(1,0) case the reality of Euclidean bosonic charges. Finally, we outline some consequences of our results, in particular for D=11 Euclidean supergravity.

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arXiv2004

Relation between quantum $κ$-Poincaré framework and Doubly Special Relativity

We describe firstly the basic features of quantum $κ$-Poincaré symmetries with their Hopf algebra structure. The quantum $κ$-Poincaré framework in any basis relates rigidly the quantum $κ$-Poincaré algebra with quantum $κ$-Poincaré group, noncommutative space-time and $κ$-deformed phase space. Further we present the approach of Doubly Special Relativity (DSR) theories, which introduce(in the version DSR1) kinematically the frame - independent fundamental mass parameter as described by maximal three-momentum $|\overrightarrow{p}|=κc$. We argue why the DSR theories in one-particle sector can be treated as the part of quantum $κ$-Poincaré framework. The DSR formulation has been extended to multiparticle states either in a way leading to nonlinear description of classical relativistic symmetries, or providing the identification of DSR approach with full quantum $κ$-Poincaré framework.

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arXiv2003

Octonionic M-theory and D=11 generalized conformal and superconformal algebras

Following [1] we further apply the octonionic structure to supersymmetric D=11 $M$-theory. We consider the octonionic $2^{n+1} \times 2^{n+1}$ Dirac matrices describing the sequence of Clifford algebras with signatures ($9+n,n$) ($n=0,1,2, ...$) and derive the identities following from the octonionic multiplication table. The case $n=1$ ($4\times 4$ octonion-valued matrices) is used for the description of the D=11 octonionic $M$ superalgebra with 52 real bosonic charges; the $n=2$ case ($8 \times 8$ octonion-valued matrices) for the D=11 conformal $M$ algebra with 232 real bosonic charges. The octonionic structure is described explicitly for $n=1$ by the relations between the 528 Abelian O(10,1) tensorial charges $Z_μZ_{μν}, Z_{μ\gt... μ_5}$ of the $M$-superalgebra. For $n=2$ we obtain 2080 real non-Abelian bosonic tensorial charges $Z_{μν}, Z_{μ_1 μ_2 μ_3}, Z_{μ_1 ... μ_6}$ which, suitably constrained describe the generalized D=11 octonionic conformal algebra. Further, we consider the supersymmetric extension of this octonionic conformal algebra which can be described as D=11 octonionic superconformal algebra with a total number of 64 real fermionic and 239 real bosonic generators.

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arXiv2003

Gravity, p-branes and a spacetime counterpart of the Higgs effect

We point out that the worldvolume coordinate functions $\hat{x}^μ(ξ)$ of a $p$-brane, treated as an independent object interacting with dynamical gravity, are Goldstone fields for spacetime diffeomorphisms gauge symmetry. The presence of this gauge invariance is exhibited by its associated Noether identity, which expresses that the source equations follow from the gravitational equations. We discuss the spacetime counterpart of the Higgs effect and show that a $p$-brane does not carry any local degrees of freedom, extending early known general relativity features. Our considerations are also relevant for brane world scenarios.

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arXiv2003

D=4 supergravity dynamically coupled to a massless superparticle in a superfield Lagrangian approach

We consider the interacting system of D=4 N=1 supergravity and the Brink-Schwarz massless superparticle as described by the sum of their superfield actions, and derive the complete set of superfield equations of motion for the coupled dynamical system. These include source terms given by derivatives of a vector superfield current density with support on the worldline. This current density is constructed from the spin 3/2 and spin 2 current density `prepotentials'. We analyze the gauge symmetry of the coupled action and show that it is possible to fix the gauge in such a way that the equations of motion reduce to those of the supergravity-bosonic particle coupled system.

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arXiv2002

On dynamical supergravity interacting with super-p-brane sources

We review recent progress in a fully dynamical Lagrangian description of the supergravity-superbrane interaction. It suggests that the interacting superfield action, when it exists, is gauge equivalent to the component action of dynamical supergravity interacting with the bosonic limit of the superbrane.

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arXiv2002

Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry

We consider a new D=2 nonrelativistic classical mechanics model providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term. In this way we provide the dynamical interpretation of the second central charge of the (2+1)-dimensional Galilean algebra. We discuss also the interpretation of k as describing the noncommutativity of D=2 space coordinates. The model is quantized in two ways: using the Ostrogradski-Dirac formalism for higher order Lagrangians with constraints and the Faddeev-Jackiw method which describes constrained systems and produces nonstandard symplectic structures. We show that our model describes the superposition of a free motion in noncommutative D=2 space as well as the "internal" oscillator modes. We add a suitably chosen class of velocity-dependent two-particle interactions, which is descrobed by local potentials in D=2 noncommutative space. We treat, in detail, the particular case of a harmonic oscillator and describe its quantization. It appears that the indefinite metric due to the third order time derivative term in the field equations, even in the presence of interactions, can be eliminated by the imposition of a subsidiary condition.

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arXiv2002

On the Superconformal Flatness of AdS Superspaces

The superconformal structure of coset superspaces with AdS_m x S^n geometry of bosonic subspaces is studied. It is shown, in particular, that the conventional superspace extensions of the coset manifolds AdS_2 x S^2, AdS_3 x S^3 and AdS_5 x S^5, which arise as solutions of corresponding D=4,6, 10 supergravities and have been extensively studied in connection with AdS/CFT correspondence, are not superconformally flat, though their bosonic submanifolds are conformally flat. We give a group-theoretical reasoning for this fact. We find that in the AdS_2 x S^2 and AdS_3 x S^3 cases there exist different supercosets based on the supergroup OSp(4^*|2) which are superconformally flat. We also argue that in D=2,3,4 and 5 there exist superconformally flat `pure' AdS_D supercosets. Two methods of checking the superconformal flatness are proposed. One of them consists in solving the Maurer-Cartan structure equations and the other is based on embedding the isometry supergroup of the AdS_m x S^n superspace into a superconformal group in (m+n)-dimensional Minkowski space. Finally, we discuss some applications of the above results to the description of supersymmetric dynamical systems.

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arXiv2002

kappa-Deformed Kinematics and Addition Law for Deformed Velocities

In kappa-deformed relativistic framework we consider three different definitions of kappa-deformed velocities and introduce corresponding addition laws. We show that one of the velocities has classical relativistic addition law. The relation of velocity formulae with the coproduct for fourmomenta and noncommutative space-time structure is exhibited.

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arXiv2002

Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory

We describe the set of generalized Poincare and conformal superalgebras in D=4,5 and 7 dimensions as two sequences of superalgebraic structures, taking values in the division algebras R, C and H. The generalized conformal superalgebras are described for D=4 by OSp(1;8| R), for D=5 by SU(4,4;1) and for D=7 by U_αU(8;1|H). The relation with other schemes, in particular the framework of conformal spin (super)algebras and Jordan (super)algebras is discussed. By extending the division-algebra-valued superalgebras to octonions we get in D=11 an octonionic generalized Poincare superalgebra, which we call octonionic M-algebra, describing the octonionic M-theory. It contains 32 real supercharges but, due to the octonionic structure, only 52 real bosonic generators remain independent in place of the 528 bosonic charges of standard M-algebra. In octonionic M-theory there is a sort of equivalence between the octonionic M2 (supermembrane) and the octonionic M5 (super-5-brane) sectors. We also define the octonionic generalized conformal M-superalgebra, with 239 bosonic generators.

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arXiv2002

Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories

The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. These unitarity constraints relate the discontinuities of amplitudes with physical intermediate states; and allow us to see how the IR/UV mixing may lead to a breakdown of unitarity. Specifically, we show that the IR/UV singularity does not lead to the violation of unitarity in the space-space noncommutative case, but it does lead to its violation in a space-time noncommutative field theory. As a corollary, noncommutative field theory without IR/UV mixing will be unitary in both the space-space and space-time noncommutative case. To illustrate this, we introduce and analyse the noncommutative Lee model--an exactly solvable quantum field theory. We show that the model is free from the IR/UV mixing in both the space-space and space-time noncommutative cases. Our analysis is exact. Due to absence of the IR/UV mixing one can expect that the theory is unitary. We present some checks supporting this claim. Our analysis provides a counter example to the generally held beliefs that field theories with space-time noncommutativity are non-unitary.

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