An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift

TL;DR

This paper introduces a novel interpretation of noncommutative field theory by decomposing coordinates into geometric and quantum shift components, providing a mapping from commutative to noncommutative theories and analyzing Lorentz-invariance violation.

Contribution

It presents a new framework for understanding noncommutative field theories through coordinate decomposition and a universal quantum shift operator.

Findings

Mapping of commutative to noncommutative field theories established

A measure for Lorentz-invariance violation derived

Coordinate decomposition into geometric and quantum shift components

Abstract

Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is introduced. A general measure for the Lorentz-invariance violation in NCFT is also derived.