A Note on UV/IR for Noncommutative Complex Scalar Field

Abstract

Noncommutative quantum field theory of a complex scalar field is considered. There is a two-coupling noncommutative analogue of U(1)-invariant quartic interaction $({\varphi }^{\ast }\varphi {)}^2$, namely $A{\varphi }^{\ast }\star \varphi \star {\varphi }^{\ast }\star \varphi +B{\varphi }^{\ast }\star {\varphi }^{\ast }\star \varphi \star \varphi$. For arbitrary values of $A$ and $B$ the model is nonrenormalizable. However, it is one-loop renormalizable in two special cases: B=0 and $A=B$. Furthermore, in the case B=0 the model does not suffer from IR divergencies at least at one-loop insertions level.

5 pages, 1 figure