Seiberg-Witten maps and scattering amplitudes of NCQED

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.

Noncommutative gauge and gravity theories and geometric Seiberg–Witten map

“…to all orders in θ) [37,40], where the power series is instead in the gauge coupling constant. For recent literature on scattering amplitudes of noncommutative particle models using the Seiberg-Witten map see [41,42] and references therein.…”