Quantization of the Szekeres System

Abstract

We study the quantum corrections on the Szekeres system in the context of canonical quantization in the presence of symmetries. We start from an effective point-like Lagrangian with two integrals of motion, one corresponding to the Hamiltonian and the other to a second rank Killing tensor. Imposing their quantum version on the wave function results to a solution which is then interpreted in the context of Bohmian mechanics. In this semiclassical approach, it is shown that there is no quantum corrections, thus the classical trajectories of the Szekeres system are not affected at this level. Finally, we define a probability function which shows that a stationary surface of the probability corresponds to a classical exact solution

7 pages, 3 figures, typos corrected in section 3.2, to appear in Classical and Quantum Gravity

References in corpus (7)

• Szekeres Swiss-Cheese model and supernova observations
• The Szekeres Swiss Cheese model and the CMB observations
• Symmetries and Singularities of the Szekeres System
• Wheeler-DeWitt quantization and singularities
• Canonical Quantization of the BTZ Black Hole using Noether Symmetries
• Dust fluid component from Lie symmetries in Scalar field Cosmology
• Modelling Inhomogeneity in Szekeres Spacetime

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• Cosmological solutions in Hořava-Lifshitz gravity
• Cyclic Szekeres Universes
• Quantum potentiality in Inhomogeneous Cosmology
• Time-covariant Schrödinger equation and invariant decay probability: The $\Lambda$-Kantowski-Sachs universe
• Symmetry Analysis In Inflationary Cosmology
• Quantum Cosmology in $f(Q)$ theory