Quantization of the Szekeres System

TL;DR

This paper investigates quantum effects on the Szekeres system using canonical quantization and finds that classical trajectories remain unaffected by quantum corrections, with a probability function aligning stationary points to classical solutions.

Contribution

It introduces a quantum analysis of the Szekeres system with symmetries, showing no quantum corrections alter classical trajectories at the semiclassical level.

Findings

Quantum corrections are absent in the semiclassical analysis.

Classical trajectories are preserved under quantum considerations.

Stationary probability surfaces correspond to classical solutions.

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