Quantum integrability of the Alday-Arutyunov-Frolov model

Author(s)

Eliane Pereira

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2015-02-12

Examining board members

Victor de Oliveira Rivelles; Gabriel Weber Martins; Aleksandr Nikolaievich Pinzul; Adilson Jose da Silva; Diego Trancanelli

• Advisor: Victor de Oliveira Rivelles; Arsen Melikyan

Abstract

In this thesis we investigate the quantum integrability of the Alday-Arutyunov-Frolov model (AAF) by diagonalization of the Hamiltonian of the AAF transformed model. The AAF transformed model is obtained from original model after fields redefinition whose purpose is to transform the Dirac brackets in the standard canonical structure between two fermions. For the diagonalization of the Hamiltonian of the transformed model we use the method developed for the Landau-Lifshitz model. This method requires regularization of the singular product of operators at the same point as well as construction of the selfadjoint extensions. We show that the wave function and the states of the transformed AAF exhibit discontinuities. We also investigated the equivalence of the matrices S of the two formulations of the AAF model through direct calculation of the S-matrix in both theories. We also consider the equivalence theorem applied to AAF model. To shows that the S matrix is invariant under field redefinitions. (AU)

• FAPESP's process: 09/17918-5 - Quantum integrability in the su(1,1) sector of string theory in AdS5xS5
• Grantee: Eliane Pereira
• Support Opportunities: Scholarships in Brazil - Doctorate