Quantum Deformation of Relativistic Symmetries: Some Recent Developments

Firstly we discuss different versions of noncommutative space-time and corresponding appearance of quantum space-time groups. Further we consider the relation between quantum deformations of relativistic symmetries and so-called doubly special relativity (DSR) theories.Comment: LaTeX, 9 pages. To appear in Proceedings of 11-th Regional Conference on Mathematical Physics, Tehran 2.05-5.05.2004, Eds. S. Rahvar, N. Sadooghi and F. Shojai, publ. World Sc. (2005

A spacetime realization of kappa-Poincare algebra

We study a Hamiltonian realization of the phase space of kappa-Poincare algebra that yields a definition of velocity consistent with the deformed Lorentz symmetry. We are also able to determine the laws of transformation of spacetime coordinates and to define an invariant spacetime metric, and discuss some possible experimental consequences.Comment: 5 pages, plain TeX. Some misprints corrected. A discussion on the possibility of experimental verifications adde

N=2 Supersymmetric Planar Particles and Magnetic Interaction from Noncommutativity

We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N=2 superfield technique and show that in the presence of a scalar N=2 superpotential the magnetic interaction is implied by the presence of noncommutativity of position variables. Further, by expressing the supersymmetric Hamiltonian as a bilinear in N=2 supercharges we obtain two supersymmetric models with electromagnetic interactions and two different noncanonical symplectic structures describing noncommutativity. We show that both models are related by a map of the Seiberg-Witten type.Comment: LaTeX,12 pages.Minor corrections; version appears in PL

Quantum Deformations of Space-Time Symmetries with Mass-Like Deformation Parameter

The difficulties with the measurability of classical space-time distances are considered. We outline the framework of quantum deformations of D=4 space-time symmetries with dimensionfull deformation parameter, and present some recent results.Comment: 4 pages, LaTeX, uses file stwol.sty, to be published in the Proceedings of XXXII International Rochester Conference in High Energy Physics (Warsaw, 24.07-31.07 1996

Transformations of coordinates and Hamiltonian formalism in deformed Special Relativity

We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets, corresponding to noncommuting spacetime coordinates.Comment: 11 pages, plain LaTe

Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras

We consider a superextension of the extended Jordanian twist, describing nonstandard quantization of anti-de-Sitter ($AdS$) superalgebra $osp(1|4)$ in the form of Hopf superalgebra. The super-Jordanian twisting function and corresponding basic coproduct formulae for the generators of $osp(1|4)$ are given in explicit form. The nonlinear transformation of the classical superalgebra basis not modifying the defining algebraic relations but simplifying coproducts and antipodes is proposed. Our physical application is to interpret the new super-Jordanian deformation of $osp(1|4)$ superalgebra as deformed D=4 $AdS$ supersymmetries. Subsequently we perform suitable contraction of quantum Jordanian $AdS$ superalgebra and obtain new $\kappa$-deformation of D=4 Poincare superalgebra, with the bosonic sector describing the light cone $\kappa$-deformation of Poincare symmetries.Comment: LaTeX,13 pages, comments and references added, to be published in Eur.Phys.J.

Acceleration-Enlarged Symmetries in Nonrelativistic Space-Time with a Cosmological Constant

By considering the nonrelativistic limit of de-Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton-Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian and Hamiltonian framework for constructing models quasi-invariant under enlarged NH symmetries which depend on three parameters described by three nonvanishing central charges. The Hamiltonian dynamics then splits into external and internal sectors with new non-commutative structures of external and internal phase spaces. We show that in the limit of vanishing cosmological constant the system reduces to the one presented in [1] which possesses accelaration-enlarged Galilean symmetries.Comment: 13 pages; small changes like a couple of footnotes et