Abstract
We calculate the Green’s functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both non-commutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two- and four-point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of non-commuting variables. The commutative part of the product does not have the mixing.
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