Discrete Nonlocal Waves

TL;DR

This paper investigates nonlocal wave solutions in a (2+1)-dimensional noncommutative scalar field theory, revealing discrete radial structures, angular momentum relations, and the absence of singularities at small scales.

Contribution

It introduces exact solutions for nonlocal waves in noncommutative space, linking nonlocality with angular momentum and showing classical behavior at large distances.

Findings

Exact standing and propagating wave solutions are derived.

Nonlocality correlates with angular momentum of fields.

No classical singularities appear at small distances.

Abstract

We study generic waves without rotational symmetry in (2+1) - dimensional noncommutative scalar field theory. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative behaviour.