Seiberg-Witten maps and scattering amplitudes of NCQED

TL;DR

This paper investigates how Seiberg-Witten maps influence scattering amplitudes in noncommutative QED, showing that reversible maps preserve amplitudes while irreversible maps cause deviations, highlighting the conditions for equivalence.

Contribution

It demonstrates that in minimal U(1) NCQED, Seiberg-Witten map interactions cancel out, maintaining amplitude equivalence, and clarifies the impact of reversible versus irreversible SW maps on scattering processes.

Findings

Reversible SW maps leave tree-level amplitudes unchanged.

Irreversible SW maps cause deviations in certain scattering amplitudes.

Tree-level amplitudes are identical before and after reversible SW maps.

Abstract

The connection between tree-level scattering amplitudes and the Seiberg-Witten (SW) map in the Moyal deformed U(1) noncommutataive quantum electrodynamics (NCQED) is studied. We show that in the minimal U(1) NCQED based on a reversible Seiberg-Witten (SW) map, SW map induced interactions cancel each other in all tree-level scattering amplitudes and leave them identical to the Moyal NCQED without SW map. On the other hand, the two-by-two Compton and light-by-light scattering amplitudes deviate from minimal model when irreversible SW map is used. Therefore the risibility of SW map and equivalence between NCQED before and after SW map manifest themselves as an identity between the tree-level scattering amplitudes.