Metric and noncommutative parameter for longitudinal spin polarization

TL;DR

This paper addresses issues in defining noncommutative momentum for longitudinal spin polarization, aiming to clarify the motivation and definitions that were previously unclear.

Contribution

The paper seeks to provide a clearer presentation and understanding of noncommutative parameters in the context of longitudinal spin polarization.

Findings

Identifies ambiguities in previous definitions of noncommutative momentum

Proposes clearer motivation and definitions for noncommutative parameters

Aims to improve conceptual understanding of spin polarization models

Abstract

There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. Therefore, this paper is withdrawn by the author for more clear presentation.