Comment on Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

TL;DR

This paper critiques a previous work on superselection rules in non-relativistic quantum mechanics, identifying a flaw in the proof regarding limitations on superposition of state vectors across different Hilbert space sectors.

Contribution

It provides a critical analysis of an existing proof, highlighting a flaw in the argument about superposition limitations due to superselection rules.

Findings

Identifies a flaw in the proof of superselection rule limitations.

Clarifies the conditions under which superposition may be restricted.

Contributes to the theoretical understanding of superselection in quantum mechanics.

Abstract

This is a comment to the paper, Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics by C Cisneros et al 1998 Eur. J. Phys. 19 237. doi:10.1088/0143-0807/19/3/005. The proof that the authors construct for the limitation on the superposition of state vectors corresponding to different sectors of the Hilbert space, partitioned by a superoperator has a flaw as outlined below.