Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework

Abstract

The Heisenberg uncertainty principle gets modified by the introduction of an observer independent minimal length. In this work we have considered the resonant gravitational wave detector in the modified uncertainty principle framework where we have used the position momentum uncertainty relation with a quadratic order correction only. We have then used the path integral approach to calculate an action for the bar detector in presence of a gravitational wave and then derived the Lagrangian of the system leading to the equation of motion for the configuration-space position coordinate in one dimension. We then find a perturbative solution for the coordinate of the detector for a circularly polarized gravitational wave leading to a classical solution of the same for given initial conditions. Using this classical form of the coordinate of the detector, we finally obtain the classical form of the on-shell action describing the harmonic oscillator-gravitational wave system. Finally, we have obtained the free particle propagator containing the quantum fluctuation term considering gravitational wave interaction.

This manuscript has been accepted for publication in "Universe"; Special Edition: "Quantum Gravity Phenomenology"

References in corpus (11)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• Universality of Quantum Gravity Corrections
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
• Quantum Black Hole and the Modified Uncertainty Principle
• Generalized uncertainty principle in resonant detectors of gravitational waves
• Probing the generalized uncertainty principle through quantum noises in optomechanical systems
• Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity
• Path integral action in the generalized uncertainty principle framework

Cited by in corpus (5)

• Minimal length scale correction in the noise of gravitons
• Uncertainty principle from the noise of gravitons
• Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework
• Lewis and Berry phases for a gravitational wave interacting with a quantum harmonic oscillator
• Gauss's Law and a Gravitational Wave