# Dynamical noncommutativity

## TL;DR

This paper introduces a dynamical noncommutativity model where the nonlocality depends on the system's energy, linking physical degrees of freedom with a dynamic noncommutative parameter.

## Contribution

It proposes a novel model of dynamical noncommutativity with energy-dependent nonlocality, integrating physical degrees of freedom and noncommutative modes.

## Key findings

- Nonlocality increases with system energy.
- Noncommutativity mode significantly influences nonlocality.
- Higher-order effects involve physical degrees of freedom.

## Abstract

The model of dynamical noncommutativity is proposed. The system consists of two interrelated parts. The first of them describes the physical degrees of freedom with coordinates q^1, q^2, the second one corresponds to the noncommutativity r which has a proper dynamics. After quantization the commutator of two physical coordinates is proportional to the function of r. The interesting feature of our model is the dependence of nonlocality on the energy of the system. The more the energy, the more the nonlocality. The lidding contribution is due to the mode of noncommutativity, however, the physical degrees of freedom also contribute in nonlocality in higher orders in \theta.