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

References in corpus (7)

• Noncommutative Perturbative Dynamics
• Magnetic fields, branes and noncommutative geometry
• Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
• Perturbative quantum gauge fields on the noncommutative torus
• Bi-local Fields in Noncommutative Field Theory
• Renormalization of noncommutative Yang-Mills theories: A simple example
• Two-Loop ${\varphi }^4$-Diagrams from String Theory

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