Noncommutative quantum mechanics of a test particle under linearized gravitational waves

2009/08/31 by Anirban Saha, Sunandan Gangopadhyay
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #hep-th

paper · pdf · doi:10.1016/j.physletb.2009.09.063

published as Phys.Lett.B681:96-99,2009 · Accepted in Physics Letters B, minor changes made, references added

openalex publication_date 2009/09/30 · arxiv created 2009/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for the interaction of gravitational wave with matter in noncommutative space is proposed. The Hamiltonian (and hence the system) is then exactly solved by using standard algebraic methods. The solutions show prominent signatures of the noncommutative nature of space. Computation of the expectation value of the particle's position reveals the inherent quantum nature of spacetime noncommutativity.

Citations

• Noncommutative Point Sources
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Stable Operation of a 300-m Laser Interferometer with Sufficient Sensitivity to Detect Gravitational-Wave Events within Our Galaxy