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Solitons, infinite symmetries and integrable field theories

Grant number: 09/16982-1
Support type:Research Projects - Thematic Grants
Duration: November 01, 2010 - October 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
Principal Investigator:José Francisco Gomes
Grantee:José Francisco Gomes
Home Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
Co-Principal Investigators:Abraham Hirsz Zimerman ; Luiz Agostinho Ferreira
Assoc. researchers: Genilson Ribeiro de Melo ; Leandro Hayato Ymai
Associated grant(s):15/50007-7 - The concept of quasi-integrability, AP.R SPRINT
14/06741-5 - Solitons in Skyrme and Skyrme-Faddeev type models, AV.EXT
13/21598-1 - The concept of quasi-integrability, AV.EXT
12/20243-2 - Integrable models with defects and Backlund transformations, AV.EXT
11/06238-3 - Vortex solutions for Yang-Mills low energy effective theories, AV.EXT
Associated scholarship(s):15/00025-9 - Backlund transformations in integrable hierarchies, solitons and integrable defects, BP.DR
12/13866-3 - Integrable defects ín field theory: classical aspects ánd quantum groups, BP.PD
11/15697-1 - Quasi-integrable field theories, BP.MS
+ associated scholarships 11/11785-3 - Solitons, infinite symmetries and integrable field theories, BP.PD
10/18110-9 - Integrable origin of higher order Painleve equations, BP.DR
10/15610-0 - Introduction tò non-linear fenomena ánd solitons, BP.IC - associated scholarships

Abstract

This project aims the study of integrable field theories, infinite dimensional algebras and soliton theory with the objective of developing methods in non-linear phenomena and non-perturbative aspects of field theories. The project is the natural continuation of the work being developed by the group in the past few years on those topics and will be implemented following two main directions. The first concerns the structure of integrable hierarchies in $1+1$ dimensions, the systematic construction of soliton solutions in terms of representation theory of Kac-Moody algebras, symmetries and its generalization to supersymmetric integrable hierarchies. The second concerns the extension of the known technology employed in constructing conserved charges and solutions in two dimensional models to theories in dimensions other than two. This is a highly nontrivial problem which may reveal new symmetries and algebraic structures important for the understanding of many non-perturbative aspects of field theories in $3+1$ dimensions. (AU)