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.

Coisotropic Branes, Noncommutativity, and the Mirror Correspondence

We study coisotropic A-branes in the sigma model on a four-torus by explicitly constructing examples. We find that morphisms between coisotropic branes can be equated with a fundamental representation of the noncommutatively deformed algebra of functions on the intersection. The noncommutativity parameter is expressed in terms of the bundles on the branes. We conjecture these findings hold in general. To check mirror symmetry, we verify that the dimensions of morphism spaces are equal to the corresponding dimensions of morphisms between mirror objects.Comment: 13 page