A New Interpretation of the Seiberg Witten Map

TL;DR

This paper presents a novel interpretation of the Seiberg-Witten map as a field-dependent coordinate transformation linking noncommutative and ordinary space-times, arising naturally from spin degrees of freedom in an extended particle model.

Contribution

It introduces a new perspective where the Seiberg-Witten map is induced by coordinate transformations related to spin, eliminating the need for ad hoc noncommutativity assumptions.

Findings

Seiberg-Witten map interpreted as a coordinate transformation

Noncommutativity emerges from spin degrees of freedom

Transformation occurs naturally in extended particle models

Abstract

In an alternative interpretation, the Seiberg-Witten map is shown to be induced by a field dependent co-ordinate transformation connecting noncommutative and ordinary space-times. Furthermore, following our previous ideas, it has been demonstrated here that the above (field dependent co-ordinate) transformation can occur naturally in the Batalin-Tyutin extended space version of the relativistic spinning particle model, (in a particular gauge). There is no need to postulate the space-time non-commutativity in an {\it ad hoc} way: It emerges from the spin degrees of freedom.