Abstract
We compute the static potential in a scalar field theory in non-commutative space including a term due to UV/IR-mixing. As a result, the potential decays exponentially fast with distance rather than like a power law as in the commutative theory due to the exchange of massless particles. This shows that when quantum effects are taken into account the introduction of non-commutativity not only modifies physics at short distances but has dramatic macroscopic consequences as well. As a result, we give a lower bound on the scale of non-commutativity (if present at all) to be compatible with power law forces over macroscopic distances.
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