Integrable theories in any dimension: a perspective

We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of dimension $d+1$ by the introduction of a $d$-form connection. The method has been used to study several theories of physical interest, like self-dual Yang-Mills theories, Bogomolny equations, non-linear sigma models and Skyrme-type models. The local version of the generalized zero curvature involves a Lie algebra and a representation of it, leading to a number of conservation laws equal to the dimension of that representation. We discuss the conditions a given theory has to satisfy in order for its associated zero curvature to admit an infinite dimensional (reducible) representation. We also present the theory in the more abstract setting of the space of loops, which gives a deeper understanding and a more simple formulation of integrability in any dimension

Ring-shaped exact Hopf solitons

The existence of ring-like structures in exact hopfion solutions is shown.Comment: version accepted for publication in JMP, includes symmetry transformation for finite paramete

Investigation of the Nicole model

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP^1 Lagrangian density to the non-integer power 3/2 - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behaviour to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.Comment: Latex, 35 pages, 1 figur

Soliton stability in some knot soliton models

We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charge (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not even critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier

Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.Comment: 64 pages, 8 figure

Neuropsychological Test Barcelona-2: Theoretical and Practical Aspects

The Barcelona test (TB) is an instrument of neuropsychological assessment, developed under the influence of Luria’s ideas, and published in 1990 [1]. It explores the main cognitive functions and allows the design of graphic profiles similar to those of the Boston Test for the diagnosis of aphasia. Objective: To present the theoretical and practical characteristics of a new version of the test, the Test Barcelona-2. The new and computerized versions of test structure is described here with six modules established: (1) Language-attention-orientation; (2) Reading and writing; (3) Motorpraxis; (4) Perception-gnosis; (5) Memory; (6) Abstraction-execution. As a novelty, test allows the selection for specific profiles: alpha, beta, abbreviated, aphasia, andecological-forensic approach. The types of variables condition a different statistical approach and a differentiated form of graphic expression. The new test presents a modular structure, which allows determining intra- and inter-module dissociations. Computerization greatly facilitates the work of the clinician. In the case of aphasia the test allows to differentiate easily all its clinical forms. Keywords: Test Barceona-2, neuropsychological test; computerized workstation, modular structur

Integrability in Theories with Local U(1) Gauge Symmetry

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.

European guidelines from the EHTG and ESCP for Lynch syndrome: an updated third edition of the Mallorca guidelines based on gene and gender

Background: Lynch syndrome is the most common genetic predisposition for hereditary cancer but remains underdiagnosed. Large prospective observational studies have recently increased understanding of the effectiveness of colonoscopic surveillance and the heterogeneity of cancer risk between genotypes. The need for gene- and gender-specific guidelines has been acknowledged. Methods: The European Hereditary Tumour Group (EHTG) and European Society of Coloproctology (ESCP) developed a multidiscipli nary working group consisting of surgeons, clinical and molecular geneticists, pathologists, epidemiologists, gastroenterologists, and patient representation to conduct a graded evidence review. The previous Mallorca guideline format was used to revise the clinical guidance. Consensus for the guidance statements was acquired by three Delphi voting rounds. Results: Recommendations for clinical and molecular identification of Lynch syndrome, surgical and endoscopic management of Lynch syndrome-associated colorectal cancer, and preventive measures for cancer were produced. The emphasis was on surgical and gastroenterological aspects of the cancer spectrum. Manchester consensus guidelines for gynaecological management were en dorsed. Executive and layperson summaries were provided. Conclusion: The recommendations from the EHTG and ESCP for identification of patients with Lynch syndrome, colorectal surveil lance, surgical management of colorectal cancer, lifestyle and chemoprevention in Lynch syndrome that reached a consensus (at least 80 per cent) are presented