Comment on "Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators"

TL;DR

This paper critically examines a recent claim in quantum mechanics, demonstrating that the assertion that quantum evolution can always be decomposed into holonomy and dynamic operators is incorrect due to logical flaws.

Contribution

It provides a rigorous critique of the previous claim, clarifying the invalidity of decomposing quantum evolution into holonomy and dynamic operators in all cases.

Findings

The claim in PRL 131, 200202 (2023) is false.

The proof of the claim relies on circular reasoning.

Quantum evolution cannot always be separated into holonomy and dynamic parts.

Abstract

We show that the claim in Ref. [PRL 131, 200202 (2023)], that the quantum time evolution always can be written as a product of a holonomy operator and a dynamic operator, is false, as it is based on a circular use of the time evolution operator.