The induced representayions of the κ\kappa-Poincare group. The massive case

The induced \6s of the $\kappa$-\1 for the massive case are described. It is shown that it extends many of the features of the classical case.Comment: AmS-Te

Lorentz-Invariant Interpretation of Noncommutative Space-Time - global version

The global version of the quantum symmetry defined by Chaichian et al (hep-th/0408069) is constructed.Comment: 5 pages, no figures. Note added pointing to the earlier work of Oeckl where the same result has been obtaine

Heisenberg algebra for restricted Landau problem

Algebraic derivation of modified Heisenberg commutation rules for restricted Landau problem is given.Comment: 6 pages, no figures,we added two references and corrected three typo

Representations of generalized oscillator algebra

The representations of the oscillator algebra introduced by Brzezinski et al. (Phys. Lett. B 311 (1993), 202) are classified.Comment: 8 pages, amste

Quantum Deformations of Space-Time SUSY and Noncommutative Superfield Theory

We review shortly present status of quantum deformations of Poincar\'{e} and conformal supersymmetries. After recalling the $\kappa$-deformation of $\hbox{D=4}$ Poincar\'{e} supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral vertices in momentum space the integration formula over $\kappa$-deformed chiral superspace is proposed.Comment: LaTeX 2e, 1 figures (included), 13 pages, Invited lecture (J.L.) at NATO Advanced Research Workshop: "Noncommutative Structure in Mathematics and Physics", Kiev, 24-27.09.2000, to be published in Pro., Kluwer Acad. Pres

The bicovariant differential calculus on the kappa-Poincare group and on the kappa-Minkowski space

The bicovariant differential calculus on the four-dimensional kappa-Poincare group and the corresponding Lie-algebra like structure are described. The deifferential calculus on the n-dimensional kappa-Minkowski space covariant under the action of the kappa-Poincare group is constructed.Comment: 9 pages,amstex,talk given by P.Maslanka on "IV Colloqium on Quantum Groups and Integrable Models ",Praque'9

Nonrelativistic conformal groups and their dynamical realizations

Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables. It is shown that the corresponding dynamical system describes, within Ostrogradski framework, the nonrelativistic particle obeying (N+1)-th order equation of motion. As a special case, the Schroedinger group and the standard Newton equations are obtained for N=1 (l=1/2).Comment: 18 pages, no figures; few references adde

Differential calculus on deformed E(2) group

Fourdimensional bicovariant differential calculus on quantum E(2) group is constructed.Comment: 8 pages, amste

Note on lattice spin in graphene and "spin from isospin" phenomenon

It is well-known that the dynamics of low energy electron in graphene honeycomb lattice near the K/K' points can be described, in tight-binding approximation, by 2+1 massless Dirac equation. Graphene's spin equivalent, "pseudospin", arises from the degeneracy introduced by the honeycomb lattice's two inequivalent atomic sites per unit cell. Mecklenburg and Regan (Phys. Rev. Lett. 106 (2011), 116803) have shown that, contrary to the common view, the pseudospin has all attributes of real angular momentum. In some circumstances, the internal symmetries can produce an important contribution to angular momentum. This phenomenon has been known for many years in particle physics and called "spin from isospin". We show that similar mechanism works in the case of lattice pseudospin

A note on the Hamiltonian formalism for higher-derivative theories

An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian is nonsingular and the Legendre transformation is performed in a straightforward way.Comment: 8 pages, no figure