Non-commutative Field Theory, Translational Invariant Products and Ultraviolet/Infrared Mixing
Abstract
We review the Moyal and Wick-Voros products, and more in general the translation invariant non-commutative products, and apply them to classical and quantum field theory. We investigate phi4 field theories calculating their Green's functions up to one-loop for the two- and four-point cases. We also review the connections of these theories with Drinfeld twists.
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