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Integrable Defects in Field Theory: Classical Aspects and Quantum Groups

Grant number: 12/13866-3
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): October 01, 2012
Effective date (End): September 30, 2015
Field of knowledge:Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
Principal Investigator:Abraham Hirsz Zimerman
Grantee:Alexis Roa Aguirre
Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
Associated research grant:09/16982-1 - Solitons, infinite symmetries and integrable field theories, AP.TEM
Associated scholarship(s):13/09969-4 - Folding in quantum groups, fusing defects and transmission matrices, BE.EP.PD

Abstract

This project concerns the study of different classical and quantum aspects of the integrable type-II defects in two-dimensional field theories. In particular, at quantum level we are interested in constructing the transmission matrices for the integrable defects allowed in Toda models associated specially with the non-simply laced affine Lie algebras B_n^{(1)} and C_n^{(1)}, by solving a linear intertwining relation between a finite dimensional representation of the relevant Borel subalgebra of the associated quantum groups U_q(G) and a particular infinite dimensional representation expressed in terms of sets of generalized quantum annihilation and creation operators. The main motivation is to describe the scattering of the solitons with the type-II defects within these kind of affine Toda models.On the other hand, the purpose of this project at classical level is to search the possible Lagrangian description of integrable type-II defects within the non-linear Schrodinger model by computing its defect matrix at higher orders in the spectral parameter and also to investigate the ''off-shell'' Hamiltonian approach for the massive Thirring model with integrable type-II defects using the r-matrix formalism or sometimes called classical and quantum inverse scattering methods.

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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
AGUIRRE, A. R.; GOMES, J. F.; YMAI, L. H.; ZIMERMAN, A. H.. N=1 super sinh-Gordon model in the half line: breather solutions. Journal of High Energy Physics, n. 4, . (12/13866-3)
AGUIRRE, A. R.; GOMES, J. F.; SPANO, N. I.; ZIMERMAN, A. H.. Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model. Journal of High Energy Physics, n. 6, . (12/13866-3)
AGUIRRE, A. R.; GOMES, J. F.; SPANO, N. I.; ZIMERMAN, A. H.. Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model. Journal of High Energy Physics, v. N/A, n. 6, p. 30-pg., . (12/13866-3)
AGUIRRE, A. R.; GOMES, J. F.; YMAI, L. H.; ZIMERMAN, A. H.. N=1 super sinh-Gordon model in the half line: breather solutions. Journal of High Energy Physics, v. N/A, n. 4, p. 23-pg., . (12/13866-3)

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