Noncommutative spin-1/2 representations

TL;DR

This paper demonstrates that noncommutative fermions can be represented as spin-1/2 under the Lorentz algebra, and derives Seiberg-Witten equations for these fermions through covariant conformal transformations.

Contribution

It extends previous work to noncommutative fermions, establishing their spin-1/2 representation and deriving related Seiberg-Witten equations.

Findings

Noncommutative fermions form a spin-1/2 Lorentz representation

Covariant splitting leads to Seiberg-Witten differential equations

Method extends previous noncommutative fermion analysis

Abstract

In this letter we apply the methods of our previous paper hep-th/0108045 to noncommutative fermions. We show that the fermions form a spin-1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations into a field-dependent part and a \theta-part implies the Seiberg-Witten differential equations for the fermions.