Cezary Gonera

Space–time symmetry of noncommutative field theory

We consider the deformed Poincare group describing the space-time symmetry of noncommutative field theory. It is shown how the deformed symmetry is related to the explicit symmetry breaking.

Differential calculi on quantum Minkowski space

The differential calculus on n‐dimensional (n≥3) quantum Minkowski space covariant with respect to left action of κ‐Poincare group is constructed and its uniqueness is shown.

On the superintegrability of TTW model

Abstract The superintegrability of so-called Tremblay–Turbiner–Winternitz (TTW) model has been conjectured on the basis of the fact that all its trajectories are closed. This conjecture has been proven using the method based on solving the partial differential equations for two functions having the same Poisson bracket with the Hamiltonian. In the present short Letter we show that superintegrability of TTW model can be established by using well-known elegant techniques of analytical mechanics. Moreover, the resulting expression (after an appropriate ordering) can be generalized to the quantum-mechanical case.

ON THE SUPERINTEGRABILITY OF CALOGERO-MOSER-SUTHERLAND MODEL

The superintegrability of Calogero-Moser-Sutherland hyperbolic model and nonsuperintegrability of trigonometric one are shown.

On the equivalence of the rational Calogero-Moser system to free particles

Abstract The canonical transformation and its unitary counterpart which relate the rational Calogero-Moser system to the free one are constructed.

Noncommutative 4-Spheres Based on all Podleś 2-Spheres and Beyond

A wide class of noncommutative spaces, including 4-spheres based on all the quantum 2-spheres and suspensions of matrix quantum groups is described. For each such space a noncommutative vector bundle is constructed. This generalises and clarifies various recent constructions of noncommutative 4-spheres.

A note on superintegrability of the quantum Calogero model

Abstract A simple proof of the superintegrability of the quantum Calogero model based on the sL(2, R ) symmetry is presented.

On the consistency of twisted gauge theory

It is argued that the twisted gauge theory is consistent provided it exhibits also the standard noncommutative gauge symmetry.

Global symmetries of noncommutative space-time

The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.

Isochronic potentials and new family of superintegrable systems

A general scheme for constructing superintegrable systems for separated Hamiltonians in an arbitrary number of degrees of freedom is presented. The resulting family contains previously known superintgrable systems with separated Hamiltonians (in Cartesian coordinates at least); however, in general, the models belonging to the family admit additional integrals which are nonpolynomial functions of momenta. An application of the method for the construction of superintegrable models of Liouville type is described.