NC plane waves, Casimir effect and flux tube potential with L\"uscher terms

TL;DR

This paper explores the effects of noncommutative geometry on quantum plane waves, revealing implications for the Casimir effect, flux tube potentials, and possible fuzzy compact dimensions, with features resembling string theory corrections.

Contribution

It introduces a model analyzing plane waves in noncommutative space, highlighting natural energy cut-offs and distance limitations affecting quantum phenomena.

Findings

Impossibility of probing distances smaller than λ

Presence of a natural energetic cut-off at 1/λ^2

Resemblance to flux tube potentials and L"uscher terms

Abstract

We analyze plane waves in a model of quantum mechanics in a three dimensional noncommutative (NC) space $R^3_{\lambda}$. Signature features of NC models are impossibility of probing distances smaller than a certain length scale {\lambda} and a presence of natural energetic cut-off at energy scale of order $1/{\lambda}^2$ (in convenient units). We analyze consequences of such restrictions on a 1 dimensional Casimir effect. The result shows resemblance to flux tube potential for quark-antiquark pairs and to effective bosonic string theories with L\"uscher terms. Such behavior might effect the radius of possible compact (fuzzy) dimensions.