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We derive a new real quantum Poincare algebra with standard real structure, obtained by contraction ofUq(0(3, 2)) (q real) , which is a standard real Hopf algebra, depending on a dimension-full parameter K instead of q. For our real quantum Poincare algebra both Casimirs are given. The free scalar K-deformed quantum field theory is considered. it appears that the K-parameter introduced nonlocal q-time derivatives with In q-1 /K.

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 ≥ 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] which describes BPS states with all but one unbroken target space supersymmetries. When 0 < a < 1 the model admits an OSp(2|8) supertwistor description, and when a > 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 sphere S 7 . *

We consider firstly simple D = 4 superalgebra with six real tensorial central charges Zµν , 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 κ-symmetries thus providing the BPS configuration preserving 3/4 of the target space supersymmetries. We show that the physical degrees of freedom (eight real bosonic and one 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 zero-superbrane model with nonvanishing mass which is generated dynamically. *

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 spaces as well as the``internal'' oscillator modes. We add a suitably chosen class of velocity-dependent twoparticle interactions, which is described 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.

The K-defonnation of the D-dimensional Poincare algebra (D ~ 2) with any signature is given. Further the quadratic Poisson brackets, determined by the classical r-matrix are calculated, and a construction of the quantum Poincare group "with noncommuting parameters" is proposed.

We consider two new classes of twisted D=4 quantum Poincaré symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincaré algebras which provide the examples of Lie-algebraic noncommutativity of the translations. The corresponding associative star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the twist deformations of Poincaré symmetries generated by the twist with its carrier in Lorentz algebra. We describe corresponding deformed Poincaré group which provides the quadratic deformations of translation sector and define the quadratically deformed Minkowski space-time algebra.