Grassmanian and Bosonic Thirring Models with Jump Defects

In this paper we discuss the Lax formulation of the Grassmanian and Bosonic Thirring models in the presence of jump defects. For the Grassmanian case, the defect is described by B\"acklund transformation which is responsible for preserving the integrability of the model. We then propose an extension of the B\"acklund transformation for the Bosonic Thirring model which is verified by some B\"acklund transitions like Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons and Two solitons - Two solitons. The Lax formulation within the space split by the defect leads to the integrability of Bosonic Thirring model.Comment: Latex 21 page

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

A new super-Backlund transformation for the N=1 supersymmetric sinh-Gordon equation is constructed. Based on this construction we propose a type-II integrable defect for the supersymmetric sinh-Gordon model consistent with this new transformation through the Lagrangian formalism. Explicit expressions for the modified conserved energy, momentum and supercharges are also computed. In addition, we show for the model that the type-II defect can also been regarded as a pair of fused defects of a previously introduced type. The explicit derivation of the associated defect matrices is also presented as a necessary condition for the integrability of the model.Comment: Latex 31 pages. Version accepted for publicatio

Between Access to Counsel and Access to Justice: A Psychological Perspective

Access to justice is a broad term that can be defined in different ways. In this volume alone we find different contributions which present different views of access to justice, and different answers to central normative questions concerning access to justice, such as how much access is appropriate, access to what exactly or access by whom. The movement to increase access to justice has likewise taken different directions, including the development of less formal forms of dispute resolution, simplification of legal processes, and the progress of in-court assistance to unrepresented litigants. Yet, traditionally, and for the most part, increasing access to justice has been related to increased access to legal counsel. Having access to representation by an attorney is considered a central means to increase individuals\u27 access to justice, i.e., access to legal institutions or to legal solutions to their problems. The ABA\u27s current proposal to institutionalize a right to counsel in certain civil cases continues this traditional movement. It offers to deal with access problems by making legal services more accessible for greater parts of society and by framing access to counsel as an entitlement in more types of cases

Thirring Model with Jump Defect

The purpose of our work is to extend the formulation of classical affine Toda Models in the presence of jump defects to pure fermionic Thirring model. As a first attempt we construct the Lagrangian of the Grassmanian Thirring model with jump defect (of Backlund type) and present its conserved modified momentum and energy expressions giving a first indication of its integrability.Comment: Poster contribution to the 5th International School on Field Theory and Gravitation, Cuiaba, MT, Brazil, 20-24 Apr 2009. to be published in PoS ISFTG(2009

Supersymmetric Construction of W-Algebras from Super Toda and Wznw Theories

A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energy-momentum tensor, is dicussed in general terms for all super Lie algebras whose simple roots are fermionic . A detailed discussion employing the Dirac bracket structure and an explicit construction of W-algebras for the cases of $OSP(1,2)$, $OSP(2,2)$ , $OSP(3,2)$ and $D(2,1 \mid \alpha )$ are given. The $N=1$ and $N=2$ super conformal algebras are discussed in the pertinent cases.Comment: 24 page

N=1 super sinh-Gordon model with defects revisited

The Lax pair formalism is considered to discuss the integrability of the N=1 supersymmetric sinh-Gordon model with a defect. We derive associated defect matrix for the model and construct the generating functions of the modified conserved quantities. The corresponding defect contributions for the modified energy and momentum of the model are explicitly computed.Comment: Latex 26 page

Generalized Miura Transformations, Two-Boson KP Hierarchies and their Reduction to KDV Hierarchies

Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV, mKdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence is taking form of the conventional Miura maps between the above KdV type of hierarchies.Comment: 12 pgs., LaTeX, IFT-P/011/93, UICHEP-TH/93-

Defects in the supersymmetric mKdV hierarchy via Backlund transformations

The integrability of the ${\cal N}=1$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super B\"acklund transformation. The construction of such transformation is performed by using essentially two methods: the B\"acklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the B\"acklund equations in components for the first few flows of the hierarchy, namely $t_3$ and $t_5$. Secondly, the supersymmetric extension of the B\"acklund transformation in the superspace formalism is constructed for those flows. Finally, this super B\"acklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.Comment: 40 pages. Some comments and references added. Version accepted for publication in JHE