On Lieb's conjecture for the Wehrl entropy of Bloch coherent states

Lieb's conjecture for the Wehrl entropy of Bloch coherent states is proved for spin 1 and spin 3/2. Using a geometric representation we solve the entropy integrals for states of arbitrary spin and evaluate them explicitly in the cases of spin 1, 3/2, and 2. We also give a group theoretic proof for all spin of a related inequality.Comment: 19 pages, LaTeX, amsfont

UV/IR mixing in noncommutative QED defined by Seiberg-Witten map

Noncommutative gauge theories defined via Seiberg-Witten map have desirable properties that theories defined directly in terms of noncommutative fields lack, covariance and unrestricted choice of gauge group and charge being among them, but nonperturbative results in the deformation parameter \theta are hard to obtain. In this article we use a \theta-exact approach to study UV/IR mixing in a noncommutative quantum electrodynamics (NCQED) model defined via Seiberg-Witten map. The fermion contribution of the one loop correction to the photon propagator is computed and it is found that it gives the same UV/IR mixing term as a NCQED model without Seiberg-Witten map.Comment: 12 page

Statistics and Quantum Group Symmetries

Using twisted realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.Comment: plain tex, 9 page

Vector Fields on Quantum Groups

We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize the construction to tensor fields. A Lie derivative along any (also non left invariant) vector field is proposed and a puzzling ambiguity in its definition discussed. These results hold for a generic Hopf algebra.Comment: 25 pages, latex, uses bezier.st