The exact renormalization group: perturbative approach and non-commutative theories

Author(s)

Ivens Martins Carneiro

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2002-04-16

Examining board members

Marcelo Otavio Caminha Gomes; Carlos Eugenio Imbassahy Carneiro; Maria Carolina Nemes

• Advisor: Marcelo Otavio Caminha Gomes

Abstract

A study of the theory of the scalar field by the methods of the Exact Renormalization Group and by the usual perturbative methods is presented, in both cases of Euclidean commutative and noncommutative spaces. A review of the main concepts underlying ERG is made, using \'\'phi\' POT. 4\' in d=4 as an illustration. Next, the perturbative renormalizability of \'\'phi\' POT. 6\' theory is presented, by the use of an equation similar to the Polchinski RG equation. Finally, the \'\'phi\' POT. 6\' theory on the Euclidean noncommutative space in d=3 is considered and the IR/UV divergencies problem is discussed, including the case of the theory with fermions and Yukawa like interactions added. (AU)