Quantum singularities in a solvable toy model

TL;DR

This paper explores how quantum mechanics can preserve classical singularities, like the Big Bang, by using simple models and introducing the concept of Kato's exceptional points as quantum singularities.

Contribution

It proposes that quantum singularities can be represented by Kato's exceptional points, challenging the idea that quantization always smooths out classical singularities.

Findings

Classical singularities can persist after quantization.

Kato's exceptional points serve as quantum analogs of classical singularities.

Elementary models demonstrate the non-smearing of singularities in quantum theory.

Abstract

Via elementary examples it is demonstrated that the singularities of classical physics (sampled by the Big Bang in cosmology) need not necessarily get smeared out after quantization. It is proposed that the role of quantum singularities can be played by the so called Kato's exceptional-point spectral degeneracies.