Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products

TL;DR

This paper compares noncommutative field theories constructed with Moyal and Wick-Voros star products, analyzing their Green's functions and S-matrix to understand their similarities and differences.

Contribution

It provides a detailed comparison of classical and quantum noncommutative field theories using two star products, highlighting their effects on Green's functions and S-matrix.

Findings

Green's functions differ between the two theories.

S-matrix is identical for both theories.

Both theories' S-matrix differs 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). 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 points 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.