Noncommutative radial waves

TL;DR

This paper investigates radial wave solutions in noncommutative scalar field theory, revealing how noncommutativity smooths out classical divergences and recovers standard behaviour at large scales.

Contribution

It introduces operatorial methods to describe radial waves in noncommutative space, showing finite series deformations of Bessel functions and the transition to commutative physics at large distances.

Findings

Radial waves propagate along a discrete radial coordinate.

Noncommutativity smooths out classical divergences.

Standard commutative behaviour is recovered at large distances.

Abstract

We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At radius much larger than the noncommutativity scale $\sqrt{\theta}$, one recovers the usual commutative behaviour. At small distances, classical divergences are smoothed out by noncommutativity.