Twisted Noncommutative Field Theory: Wick-Voros vs Moyal

TL;DR

This paper compares noncommutative field theories constructed with Moyal and Wick-Voros star products, revealing differences in Green's functions but equivalence in S-matrix outcomes, highlighting subtle distinctions in noncommutative geometry.

Contribution

It provides a detailed comparison of two noncommutative field theories, showing that despite different Green's functions, their S-matrix results are identical, advancing understanding of noncommutative geometries.

Findings

Green's functions differ between the two theories.

S-matrix is identical for both theories.

Both theories differ from the commutative case.

Abstract

We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). 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.