Quantum Mechanics on Noncommutative Spacetime

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.

8 pages

References in corpus (2)

• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• Symmetries, Microcausality and Physics on Canonical Noncommutative Spacetime

Cited by in corpus (11)

• Magnetic fields in noncommutative quantum mechanics
• The Noncommutative Anandan's Quantum Phase
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Tensor Operators in Noncommutative Quantum Mechanics
• Dynamical symmetries in noncommutative theories
• Deformed squeezed states in noncommutative phase space
• Tensor Coordinates in Noncommutative Mechanics
• A new kind of representations on noncommutative phase space
• Localization at threshold in noncommutative space
• Inverse square problem and so(2,1) symmetry in noncommutative space
• Non-commutativity as a measure of inequivalent quantization