arXiv subjects

Manolo Rivera

Publications and source records attributed to Manolo Rivera.

2 recordsLinked to original sources

arXiv2015

Noncommutative Field Theory With General Translation Invariant Star Products

We compute the two-point and four-point Green's function of the noncommutative $ϕ^{4}$ field theory; first with the s-ordered star products and then with a general translation invariant star product. We derive the differential expression for any translation invariant star product, and with the help of this expression we show that any of these products can be written in terms of a twist. Finally, using the notion of the twisted action of the infinitesimal Poincaré transformations, we show that the commutator between the coordinate functions is invariant under Poincaré transformations at a deformed level.

hep-th↗

arXiv2015

Green's Functions for Translation Invariant Star Products

We calculate the Green 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 noncommutative 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 noncommuting variables. The commutative part of the product does not have the mixing.

hep-th↗