Coherent States and N Dimensional Coordinate Noncommutativity

TL;DR

This paper develops a framework where coordinates as operators exhibit noncommutativity and full N-dimensional rotation invariance, with fluctuations controlled by two scales, potentially testable by LIGO.

Contribution

It introduces a gauge-invariant theory of coordinate noncommutativity based on SO(N,1) coherent states, extending previous models to include translation invariance in N dimensions.

Findings

Coordinates exhibit noncommutativity with rotation invariance.

Fluctuations are fixed at the noncommutativity scale for small distances.

Large-distance fluctuations are proportional to distance divided by a large number.

Abstract

Considering coordinates as operators whose measured values are expectations between generalized coherent states based on the group SO(N,1) leads to coordinate noncommutativity together with full $N$ dimensional rotation invariance. Through the introduction of a gauge potential this theory can additionally be made invariant under $N$ dimensional translations. Fluctuations in coordinate measurements are determined by two scales. For small distances these fluctuations are fixed at the noncommutativity parameter while for larger distances they are proportional to the distance itself divided by a {\em very} large number. Limits on this number will lbe available from LIGO measurements.