Quantum gauge theories on noncommutative three-dimensional space

We consider a class of gauge-invariant models on the noncommutative space ℝ3λ, a deformation of the algebra of functions on ℝ3. Focusing on massless models with no linear Ai dependence, we obtain noncommutative gauge models for which the computation of the propagator can be done in a convenient gauge. We find that the infrared singularity of the massless propagator disappears in the computation of the correlation functions. We show that massless gauge-invariant models on ℝ3λ have quantum instabilities of the vacuum, signaled by the occurrence of nonvanishing one-point functions for some but not all of the components of the gauge potential. The tadpole contribution to the effective action cannot be interpreted as a standard σ term. Its global symmetry does not fit with the one of the classical action, reminiscent of an explicit global symmetry breaking term.