Noncommutative quantum mechanics of a test particle under linearized gravitational waves

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.

Accepted in Physics Letters B, minor changes made, references added

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• Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space
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• Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework
• Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective
• Signatures of noncommutativity in bar detectors of gravitational waves
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework
• Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves
• Lewis and Berry phases for a gravitational wave interacting with a quantum harmonic oscillator
• Quantum mechanics of a charged particle in a background magnetic field interacting with linearized gravitational waves
• Interaction of a circularly polarised gravitational wave with a charged particle in a static magnetic background
• Quantum mechanical interaction of matter with the scalar mode of gravitational wave in modified gravity theories