Interactions between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field

Consistent couplings between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field are analyzed in the framework of Lagrangian BRST cohomology. Under the assumptions on smoothness, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interacting Lagrangian is at most second-order derivative, it is proved that there are no consistent cross-interactions between a single massless tensor field with the mixed symmetry of the Riemann tensor and one massless vector field.Comment: LaTeX, 24 page

Effects of extended impurity perturbation in d-wave superconductor

We describe the effects of electronic perturbation distributed on nearest neighbor sites to the impurity center in a planar \textit{d}-wave superconductor, in approximation of circular Fermi surface. Alike the behavior previously reported for point-like perturbation and square Fermi surface, the quasiparticle density of states $\rho (\epsilon)$ can display a resonance inside the gap (and very weak features from low symmetry representations of non-local perturbation) and asymptotically vanishes at $\epsilon \to 0$ as $\rho\sim\epsilon/\ln^2\epsilon$. The local suppression of SC order parameter in this model is found to be somewhat weaker than for an equivalent point-like (non-magnetic) perturbation and much weaker than for a spin-dependent (extended) perturbation.Comment: 7 pages, 5 figures, some minor typos and the curves in Fig. 5 correcte