Free Field Realization of Vertex Operators for Level Two Modules of Uq(sl(2)^)U_q(\hat{sl(2)})

Free field relization of vertex operators for lvel two modules of $U_q(\hat{sl(2)})$ is shown through the free field relization of the modules given by Idzumi in Ref.[4,5]. We constructed types I and II vertex operators when the spin of the addociated evaluation modules is 1/2 and typ II's for the spin 1.Comment: 15 pages, to appear in J.Phys.A:Math and Genera

The sine-Gordon model with integrable defects revisited

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment

The SO(N) principal chiral field on a half-line

We investigate the integrability of the SO(N) principal chiral model on a half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in involution. We use an anomaly-counting method to show that at least one non-trivial example survives quantization, compare our results with the proposed reflection matrices, and, based on these, make some preliminary remarks about expected boundary bound-states.Comment: 7 pages, Late

Form factors of boundary fields for A(2)-affine Toda field theory

In this paper we carry out the boundary form factor program for the A(2)-affine Toda field theory at the self-dual point. The latter is an integrable model consisting of a pair of particles which are conjugated to each other and possessing two bound states resulting from the scattering processes 1 +1 -> 2 and 2+2-> 1. We obtain solutions up to four particle form factors for two families of fields which can be identified with spinless and spin-1 fields of the bulk theory. Previously known as well as new bulk form factor solutions are obtained as a particular limit of ours. Minimal solutions of the boundary form factor equations for all A(n)-affine Toda field theories are given, which will serve as starting point for a generalisation of our results to higher rank algebras.Comment: 24 pages LaTeX, 1 figur

Linearisation of Universal Field Equations

The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the conjecture that these equations describe integrable systems. While this construction is implicit in general, there exists a large class of solutions for which an explicit form may be written.Comment: 11pp., DTP-92/47, NI-92/01

Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras

We show that a suitable coset algebra, constructed in terms of an extension of the Zamolodchikov-Faddeev algebra, is homomorphic to the Reflection-Transmission algebra, as it appears in the study of integrable systems with impurity.Comment: 8 pages; a misprint in eq. (2.14) and (2.15) has been correcte

Knockout of CXCR5 increases the population of immature neural cells and decreases proliferation in the hippocampal dentate gyrus

BACKGROUND The process of neurogenesis in which new neurons are generated by proliferation and differentiation of neural stem/progenitor cells (NSCs/NPCs) has been a topic of intensive recent investigation. Investigations of the factors which regulate this process have recently begun to include immune factors including immune cells and cytokines, however the class of immune proteins designated as chemokines have been relatively neglected. Increasing evidence for novel brain-specific mechanisms of chemokines beyond their classical chemotactic functions has suggested that they may play a role in the regulation of NSC/NPC biology. METHODS We have investigated the role of the chemokine receptor CXCR5 (ligand is CXCL13) in the activity of these cells through neurobiological and behavioural analysis of CXCR5-deficient mice (CXCR5-/-). These investigations included: immunohistochemistry for the markers Ki67, nestin, doublecortin, and IBA-1, neurosphere assays, and the baseline behavioural tests: open field test and sucrose preference test. RESULTS We observed a significant increase in doublecortin and nestin staining in the hippocampal dentate gyrus (P = 0.02 and P = 0.0008, respectively) of CXCR5-/- animals as compared to wild-type controls. This was accompanied by a decrease in Ki67 staining subgranular zone (P = 0.009). Behavioural correlates included a significant increase in baseline locomotor activity in an open field test (P <0.00018) and a decrease in stress reactivity in that test (P = 0.015). Deficiency in CXCR5 was not associated with alterations in hippocampal microglial density, microglial activation or systemic cytokine levels, nor with loss of NSC/NPC populations in the neurosphere assay. CONCLUSIONS These findings are the first to describe a brain-specific function of CXCR5 under physiological conditions. CXCR5 reduces maintenance of immature neural cell populations and enhances proliferation of subgranular zone cells in the hippocampal dentate gyrus, however the mechanism of these effects remains unclear. Further research into the regulation of NSC/NPC activity should consider investigation of CXCR5 and other chemokines which may be relevant to the pathophysiology of psychiatric disorders including depression, anxiety and cognitive impairment/dementia.Michael J Stuart, Frances Corrigan and Bernhard T Baun

Liouville integrable defects: the non-linear Schrodinger paradigm

A systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrodinger model in the presence of a single particle-like defect is investigated through this algebraic approach. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. Coincidence of our results with the continuum limit of the discrete expressions obtained in earlier works further confirms our approach.Comment: 22 pages, Latex. Minor misprints correcte

The quantum non-linear Schrodinger model with point-like defect

We establish a family of point-like impurities which preserve the quantum integrability of the non-linear Schrodinger model in 1+1 space-time dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the space-time symmetry of the bulk scattering matrix, are also discussed.Comment: Comments on the integrability and the impurity free limit adde