Twisted noncommutative field theory with the Wick-Voros and Moyal products

We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). For the latter we discuss both the classical and the quantum field theory in the quartic potential case and calculate the Green’s functions up to one loop, for the two- and four-point cases. We compare the two theories in the context of the noncommutative geometry determined by a Drinfeld twist, and the comparison is made at the level of Green’s functions and $S$ matrix. We find that while the Green’s functions are different for the two theories, the $S$ matrix is the same in both cases and is different from the commutative case.

Figure 1

The (a) planar and (b) nonplanar one-loop correction to the propagator.

Figure 2

The planar one-loop four-point diagram.

Figure 3

The nonplanar one-loop four-point diagrams.

Figure 4

The two-particle elastic scattering.