A note on the action-angle variables for the rational Calogero-Moser system

A relationship between the action-angle variables and the canonical transformation relating the rational Calogero-Moser system to the free one is discussed.Comment: 6 pages, LaTeX. Acknowledgments are slightly altere

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.Comment: 7 pages, no figures;two references adde

A gauge theory of the hamiltonian reduction for the rational Calogero - Moser system

A gauge theory equivalent to the hamiltonian reduction scheme for rational Calogero - Moser model is presented.Comment: LaTeX, 2 figures. To appear in Phys.Lett.

N=1/2 Global SUSY: R-Matrix Approach

R-matrix method is used to construct supersymmetric extensions of theta - Euclidean group preserving N = 1/2 supersymmetry and its three- parameter generalization. These quantum symmetry supergroups can be considered as global counterparts of appropriately twisted Euclidean superalgebras. The corresponding generalized global symmetry transformations act on deformed superspaces as the usual ones do on undeformed spaces. However, they depend on non(anti)commuting parameters satisfying (anti)commutation relations defined by relevant R matrix.Comment: 30 pages, a number of typos corrected; two references adde

On determination of statistical properties of spectra from parametric level dynamics

We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of statistical physics, proposed previously in the literature, taking into account appropriate integrals of motion of the parametric dynamics is fully justified, even if the used integrals of motion do not determine the invariant manifold in a unique way. The indetermination of the manifold is removed by applying Dirac's theory of constrained Hamiltonian systems and imposing appropriate primary, first-class constraints and a gauge transformation generated by them in the standard way. The obtained results close the gap in the whole reasoning aiming at understanding statistical properties of spectra in terms of parametric dynamics.Comment: 9 pages without figure