The model CPN-1 non-commutative in (2 +1) D

Author(s)

Alexandre Guimarães Rodrigues

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2003-12-18

Examining board members

Marcelo Otavio Caminha Gomes; Antônio José Accioly; Dionisio Bazeia Filho; Fernando Tadeu Caldeira Brandt; Victor de Oliveira Rivelles

• Advisor: Marcelo Otavio Caminha Gomes

Abstract

In this thesis investigate possible extensions of the (2+1) dimensional CPN-1 model to the noncommutative space. Up to leading nontrivial order of 1/N, we prove that the model restricted to the left fundamental representation is renormalizable and does not have dangerous infrared divergences. By contrast, IF the pricipal Field transforms in accord with the adjoint representation, linearly divergent, nonintegrable singularities are present in the two point function of the auxiliary gauge Field and also in the leading correction to the self-energy of the Field. It is showed that the inclusion of fermionic matter, minimally coupled to the gauge Field, ameliorates this behavior by eliminating infrared divergences in the gauge sector at the leading 1/N order. Gauge invariance of the renormalization is also discussed. (AU)