from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. The condition of being noncommutative
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Now we know for sure that it's not our ignorance at fault (as you seem to suggest), but rather that it is an intrinsic property of quantum mechanics, which, incidentally, is related to the noncommutativity of rotations in three dimensions.
Have you ever experienced noncommutativity of observations?
In the case of noncommutative gauge theory, we get a theory that is widely believed (or known?) to be UV-finite, even though it looks as a deformation by a dimension 6 operator at low energies (recall that when you expand the star product, the first non-trivial term will have two extra derivatives in it, multiplied by theta, the noncommutativity = commutator of