Quantum Mechanics on Noncommutative Spacetime

TL;DR

This paper derives a quantum mechanical Hamiltonian on noncommutative spacetime, revealing an intrinsic electric dipole moment that does not affect current EDM experiments, challenging previous bounds on noncommutative scales.

Contribution

It provides a non-relativistic Hamiltonian for quantum mechanics on noncommutative spacetime and clarifies the observational implications of intrinsic electric dipole moments.

Findings

Intrinsic electric dipole moments are spin independent.

Current EDM experiments cannot detect noncommutative effects.

Previous bounds on noncommutative scales are invalidated.

Abstract

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note however that noncommutative intrinsic dipole moments are not observable in present experiments searching for an EDM of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moment are thus incorrect.