Quantum mechanics and geodesic deviation in the brane world

Abstract

We investigate the induced geodesic deviation equations in the brane world models, in which all the matter forces except gravity are confined on the 3-brane. Also, the Newtonian limit of induced geodesic deviation equation is studied. We show that in the first Randall-Sundrum model the Bohr-Sommerfeld quantization rule is as a result of consistency between the geodesic and geodesic deviation equations. This indicates that the path of test particle is made up of integral multiples of a fundamental Compton-type unit of length $h/mc$.

5 pages, no figures

References in corpus (7)

• Lorentz invariance with an invariant energy scale
• Classical and quantum dynamics of confined test particles in brane gravity
• Classical and quantized aspects of dynamics in five dimensional relativity
• Stabilization of test particles in Induced Matter Kaluza-Klein theory
• Space-Time Uncertainty from Higher-Dimensional Determinism (or: How Heisenberg was right in 4D because Einstein was right in 5D)
• Non-integrability and Mach's principle in Induced Matter Theory
• Semiclassical corrections to the Einstein equation and Induced Matter Theory

Cited by in corpus (7)

• Geodesic deviation in Saez--Ballester theory
• Noncompactified Kaluza--Klein Gravity
• Geodesic deviation equation in Brans-Dicke theory in arbitrary dimensions
• Cosmic Acceleration and Geodesic Deviation in Chameleon Scalar Field Model
• Geodesic deviation equation in generalized hybrid Metric-Palatini gravity
• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
• Intrinsic quantum dynamics of particles in brane gravity