Selfconsistent effective interactions and symmetry restoration

In this paper we propose a general framework for deriving the effective interactions for many-body systems. We show how the selfconsistent interaction can be constructed on the quantum level for both local and nonlocal potentials. In particular the relation between the selfconsistent and symmetry restoring interaction is derived. The difference between the two is related to the coupling of the perturbing field to the kinetic energy operator.Comment: 4 pages, revtex file, no figures, submitted to Phys. Rev. Let

Emergent Supersymmetry in Warped Backgrounds

We show that quantum mechanical supersymmetries are emerged in Kaluza-Klein spectrum of linearized gravity in several warped backgrounds as a consequence of higher-dimensional general coordinate invariance. These emergent supersymmetries play an essential role for the spectral structure of braneworld gravity. We show that for the case of braneworld models with two codimension-1 branes the spectral pattern is completely determined only through the supersymmetries

Explicit formula for singular vectors of the Virasoro algebra with central charge less than 1

We calculate explicitly the singular vectors of the Virasoro algebra with the central charge $c\leq 1$. As a result, we have an infinite sequence of the singular vectors for each Fock space with given central charge and highest weight, and all its elements can be written in terms of the Jack symmetric functions with rectangular Young diagram.Comment: 10 pages, revised versio

Studies on Bile Pigments II. Seperation of Natural Direct Bilirubins

Separation of both forms of the direct bilirubin were carried out from the dog's gallbladder bile, and further isolations of them were also done. 1. The natural salt-form bilirubin was isolated after separation on the column of aluminium oxide with a n-propanolic aqueous solution. 2. The natural salt-form bilirubin was obtained in amorphous yellow powders which were strongly hygroscopic and easily soluble in water and methanol but not in chloroform or carbon tetrachloride. An aqueous solution of these powders showed both the direct diazo and Gmelin reaction, but neither Ehrlich's aldehyde nor Schlesinger reaction. The salt-form bilirubin was transferred into chloroform only when some quantities of hydrochloric acid were added to a mixture of chloroform and an aqueous solution of it. 3. The absorption maxima of the natural salt-form bilirubin existed at 420 to 430 m&#956; in a methanolic solution and at 425 or 435m&#956; in 50% or 10% n-propanol. 4. The natural ester-form bilirubin was isolated after separating on the column of silica gel with a chloroformethanolic mixture. 5. The natural ester-form bilirubin was obtained in amorphous greenish yellow powders. It was further hygroscopic and easily soluble in water and methanol but not in chloroform or carbon tetrachloride. An aqueous solution of it showed the direct diazo and Gmelin reaction, but neither Ehrlich's aldehyde nor Schlesinger's reaction. No pigment was transferred into chloroform even if some quantities of hydrochloric acid were added to a mixture of chloroform and an aqueous solution of it, but did by saponification with 5% methanolic potash. 6. The absorption maxima of the natural ester-form bilirubin existed at 415 m&#956; in both methanolic and aqueous solutions.</p