Physical mathematics of integrable systems

• Grant number: 09/01804-0
• Support Opportunities: Research Projects - Thematic Grants
• Start date: July 01, 2009
• End date: June 30, 2013
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Marcio Jose Martins
• Grantee: Marcio Jose Martins
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Giuliano Augustus Pavan Ribeiro
• Associated research 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)