Functional Integral Construction of the Massive Thirring model: Verification of Axioms and Massless Limit

We present a complete construction of a Quantum Field Theory for the Massive Thirring model by following a functional integral approach. This is done by introducing an ultraviolet and an infrared cutoff and by proving that, if the “bare” parameters are suitably chosen, the Schwinger functions have a well defined limit satisfying the Osterwalder-Schrader axioms, when the cutoffs are removed. Our results, which are restricted to weak coupling, are uniform in the value of the mass. The control of the effective coupling (which is the main ingredient of the proof) is achieved by using the Ward Identities of the massless model, in the approximated form they take in the presence of the cutoffs. As a byproduct, we show that, when the cutoffs are removed, theWard Identities have anomalies which are not linear in the bare coupling. Moreover, we find for the interacting propagator of the massless theory a closed equation which is different from that usually stated in the physical literature.     

Crosslinking Allosteric Sites on the Nucleosome

Targeting defined histone protein sites in chromatin is an emerging therapeutic approach that can potentially be enhanced by allosteric effects within the nucleosome. Here we characterized a novel hetero‐bimetallic compound with a design based on a nucleosomal allostery effect observed earlier for two unrelated drugs—the Ru^II antimetastasis/antitumor RAPTA‐T and the Au^I anti‐arthritic auranofin. The Ru^II moiety binds specifically to two H2A glutamate residues on the nucleosome acidic patch, allosterically triggering a cascade of structural changes that promote binding of the Au^I moiety to selective histidine residues on H3, resulting in cross‐linking sites that are over 35 Å distant. By tethering the H2A‐H2B dimers to the H3‐H4 tetramer, the hetero‐bimetallic compound significantly increases stability of the nucleosome, illustrating its utility as a site‐selective cross‐linking agent.     

Molecular Kondo resonance in atomic Fermi gases

The usual Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. We show, however, that also a bosonic form of the Kondo effect can occur in degenerate atomic Fermi gases near a Feshbach resonance, if the energy of the diatomic molecular level associated with the Feshbach resonance approaches twice the Fermi energy of the atoms.     

Preconcentration and dansylation of aliphatic amines using C18 solid-phase packings. Application to the screening analysis in environmental water samples

Precolumn preconcentration and derivatization on solid sorbents (Bond Elut C18 solid-phase extraction cartridges) of low-molecular-mass aliphatic amines in water samples have been performed using dansyl chloride (Dns-Cl) as derivatization reagent. Conditions for analyte preconcentration and derivatization such as volume sample, reagent concentration, time, pH and temperature reaction were optimised. On the basis of these studies a rapid and sensitive method for screening of aliphatic amines in waters is presented. Up to volumes of 5 ml, samples are drawn through the sorbent, the analytes retained are dansylated at basic pH, at 100 degrees C for 10 min or 85 degrees C for 15 min. The derivatized analytes are desorbed with 0.5 ml of acetonitrile. Twenty microl of the collected extracts are chromatographed in a Hypersyl ODS C18 column using an acetonitrile-imidazole (pH 7) gradient for elution. Seven amines and ammonium were separated within 9 min. The Dns derivatives were monitored at 333 nm with UV detection and at lambda(excitation) = 350 nm and lambda(emission) = 530 nm with fluorescence detection. The different signals are compared. Dynamic ranges from 10 to 250 microg/l and limits of detection at the microgram-per-litre level and relative standard deviations from 2 to 15% were obtained for all the amines. The total analysis time (sample treatment plus chromatography) was less than 25 min. The method was applied to determination and screening analysis of these analytes in real environmental water samples.     

The Schur property for subgroup lattices of groups

A classical theorem of Schur states that if the centre of a group G has finite index, then the commutator subgroup G′ of G is finite. A lattice analogue of this result is proved in this paper: if a group G contains a modularly embedded subgroup of finite index, then there exists a finite normal subgroup N of G such that G/N has modular subgroup lattice. Here a subgroup M of a group G is said to be modularly embedded in G if the lattice is modular for each element x of G. Some consequences of this theorem are also obtained; in particular, the behaviour of groups covered by finitely many subgroups with modular subgroup lattice is described. Received: 16 October 2007, Final version received: 22 February 2008     

Groups with finitely many normalizers of non-periodic subgroups

A theorem of Polovickiĭ states that any group with finitely many normalizers of subgroups is finite over its centre. Here we prove that the centre of a non-periodic group G has finite index if and only if G has finitely many normalizers of non-periodic subgroups.     

Detecting the index of a subgroup in the subgroup lattice

A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if  is a group and is a subgroup of finite index of , the index cannot be recognized in the lattice of all subgroups of , as for instance all groups of prime order have isomorphic subgroup lattices. The aim of this paper is to give a lattice-theoretic characterization of the number of prime factors (with multiplicity) of .