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Physical mathematics of integrable systems

Grant number: 09/01804-0
Support type:Research Projects - Thematic Grants
Duration: July 01, 2009 - June 30, 2013
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal Investigator:Marcio Jose Martins
Grantee:Marcio Jose Martins
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Assoc. researchers:Giuliano Augustus Pavan Ribeiro
Associated grant(s):10/08797-7 - Integrable lattice models based on super groups, AV.EXT
Associated scholarship(s):10/19839-2 - Algebraic curves of integrable models: theory and applications, BP.DR

Abstract

This research proposal intends to investigate several aspects related to the Physical Mathematics of two-dimensional integrable models. We will consider the exact solution of vertex models of Statistical Mechanics based on the Uq[SU(2)] quantum group at roots of unity, on the classical exceptional Lie algebras and superalgebras, on the non-compact SL(2,R) algebra as well as extensions of the Hubbard Model. In these systems we shall study both their mathematical properties of integrability and their potential applications to Field Theory and Condensed Matter. We hope to apply and to develop tools that will help us to unveil the physical behaviour of integrable systems such as the nature of their elementary excitations, thermodynamics and correlation unctions of observables. (AU)