Geometry of a Quantized Spacetime: The Quantum Potential Approach

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Mirza, Babur M.^1

Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan^1

关键词: Black-hole spacetimes;    Curved spacetime;    Gaussian Wave Packets;    Modified Lagrangian;    Quantum dynamics;    Quantum effects;    Quantum potentials;    Quantum soliton;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012198/pdf
DOI  :  10.1088/1742-6596/490/1/012198

来源: IOP

【 摘 要 】

Quantum dynamics in a curved spacetime can be studied using a modified Lagrangian approach directly in terms of the spacetime variables [Mirza, B.M., Quantum Dynamics in Black Hole Spacetimes, IC-MSQUARE 2012]. Here we investigate the converse problem of determining the nature of the background spacetime when quantum dynamics of a test particle is known. We employ the quantum potential formalism here to obtain the modifications introduced by the quantum effects to the background spacetime. This leads to a novel geometry for the spacetime in which a test particle modifies the spacetime via interaction through the quantum potential. We present here the case of a Gaussian wave packet, and a localized quantum soliton, representing the test particle, and determine the corresponding geometries that emerge.