Nilpotent noncommutativity and renormalization

Abstract

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizablility properties of NC theories.

5 figures, a reference added

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Cited by in corpus (6)

• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• The number of eigenstates: counting function and heat kernel
• Noncommutativity due to spin
• Photon propagation in noncommutative QED with constant external field
• Renormalization on noncommutative torus
• Quantum Space-Time and Noncommutative Gauge Field Theories