Non-commutative Field Theory, Translational Invariant Products and Ultraviolet/Infrared Mixing

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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This work was performed for the fulfilment of the requirements for the degree of Doctor of Philosophy at the Universit\`{a} di

Scientific paper

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.

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