A note on the proof of magnetic flux quantization from ODLRO

TL;DR

This paper identifies an imperfection in a recent proof linking magnetic flux quantization to ODLRO and proposes a corrected proof to address the issue.

Contribution

It provides a corrected proof of magnetic flux quantization from ODLRO, fixing a mathematical inconsistency in previous work.

Findings

Identified a flaw in the previous proof involving f-factors.

Proposed a mathematically consistent corrected proof.

Clarified the conditions under which flux quantization holds.

Abstract

It is noticed that the excellent proof of the connection of magnetic flux quantization and off-diagonal long range order (ODLRO) presented recently by Nieh, Su and Zhao suffers from an imperfection, namely, the f-factors in the case of finite translation do not satisfy $f(a)f(b)=f(a+b)$, which was employed in the proof. A corrected proof is proposed to remedy this point.