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 Poincar\'{e} 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 ($\theta_{\mu\nu}$-deformation) and second with Lie-algebraic structure of quantum space-time, introducing so-called $\kappa$-deformation. The third fundamental constant of Nature - fundamental mass $\kappa$ or length $\lambda$ - appears naturally in proposed quantum relativistic symmetry scheme. The deformed Minkowski space is described as the representation space (Hopf-module) of deformed Poincar\'{e} algebra. Some possible perspectives of quantum-deformed relativistic symmetries will be outlined.Comment: LaTeX, 8 pages, AIP Proceedings style (included). Submitted to the Proceedings of Albert Einstein Century International Conference, July 18--22, 2005, Pari

Massive twistor particle with spin generated by Souriau-Wess-Zumino term and its quantization

We present new model of D=4 relativistic massive particle with spin and we describe its quantization. The model is obtained by an extension of standard relativistic phase space description of massive spinless particle by adding new topological Souriau-Wess-Zumino term which depends on spin fourvector variable. We describe equivalently our model as given by the free two-twistor action with suitable constraints. An important tool in our derivation is the spin-dependent twistor shift, which modifies standard Penrose incidence relations. The quantization of the model provides the wave function with correct mass and spin eigenvalues.Comment: 1+15 page

Higher Spins from Nonlinear Realizations of OSp(1∣8)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.Comment: LaTeX, 13 pages. Minor, mostly typographic corrections. Version which appears in Physics Letters