Poisson brackets and Poisson spectra in polynomial algebras

Poisson brackets on the polynomial algebra C[x,y,z] are studied. A description of all such brackets is given and, for a significant class of Poisson brackets, the Poisson prime ideals and Poisson primitive ideals are determined. The results are illustrated by numerous examples.Comment: includes minor corrections to published versio

Axial anomaly and the delta_{LT} puzzle

The axial anomaly contribution to generalized longitudinal-transverse polarizability $\delta_{LT}^{}$ is calculated within Regge approach. It is shown that the contribution from the exchange of the $a_1^{}(1260)$ Regge trajectory is nontrivial and might have the key role to explain the large difference between the predictions of chiral perturbation theory and the experimental data for the neutron $\delta_{LT}^{}$. We also present the prediction for the proton $\delta_{LT}^{}$, which will be measured at the Thomas Jefferson National Accelerator Facility in near future.Comment: 5 pages, 3 figures, REVTeX, to be published in Phys. Rev.

The spin-split incompressible edge states within empirical Hartree approximation at intermediately large Hall samples

A self-consistent Thomas-Fermi-Poisson based calculation scheme is used to achieve spin resolved incompressible strips (ISs). The effect of exchange and correlation is incorporated by an empirically induced g factor. A local version of the Ohm's law describes the imposed fixed current, where the discrepancies of this model are resolved by a relevant spatial averaging process. The longitudinal resistance is obtained as a function of the perpendicular (strong) magnetic field at filling factor one and two plateaus. Interrelation between the ISs and the longitudinal zeros is explicitly shown.Comment: EP2DS-17 Proceedings, 6 Pages, 2 Figure