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 $(ϕ^*ϕ)^2$, namely $Aϕ^*\starϕ\starϕ^*\starϕ+ Bϕ^*\starϕ^*\starϕ\starϕ$. 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.