Noncommutative quantum mechanics and Bohm's ontological interpretation

TL;DR

This paper explores a Bohmian interpretation of noncommutative quantum mechanics, analyzing particle motion and implications for noncommutativity, with detailed study of the noncommutative harmonic oscillator.

Contribution

It develops a consistent Bohmian framework for noncommutative quantum mechanics and examines its effects on particle dynamics and large-scale physics.

Findings

Bohmian interpretation conditions are established for noncommutative quantum mechanics.

Particle motion in the noncommutative harmonic oscillator is analyzed in detail.

Small-scale physics influences large-scale behavior, akin to IR-UV mixing.

Abstract

We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing.