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 phi^4 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.

This work was performed for the fulfilment of the requirements for the degree of Doctor of Philosophy at the Università di Napoli Federico II.