# Kinematic variables in noncommutative phase space and parameters of noncommutativity

## TL;DR

This paper investigates how noncommutativity of coordinates and momenta in phase space affects the properties of kinematic variables, and identifies conditions that preserve fundamental physical principles.

## Contribution

It derives conditions on noncommutativity parameters ensuring that kinematic variables behave correctly and fundamental principles like the weak equivalence principle are maintained.

## Key findings

- Coordinates depend on mass in noncommutative phase space
- Noncommutative momenta are not proportional to mass
- Conditions are found that preserve the weak equivalence principle and proper kinetic energy properties

## Abstract

We consider a space with noncommutativity of coordinates and noncommutativity of momenta. It is shown that coordinates in noncommutative phase space depend on mass therefore they can not be considered as kinematic variables. Also, noncommutative momenta are not proportional to a mass as it has to be. We find conditions on the parameters of noncommutativity on which these problems are solved. It is important that on the same conditions the weak equivalence principle is not violated, the properties of kinetic energy are recovered, and the motion of the center-of-mass of composite system and relative motion are independent in noncommutative phase space.