**几何动量十周年**精选

论文 https://arxiv.org/abs/2103.03408, The curvature-induced gauge potential and the geometric momentum for a particle on a hypersphere (曲率诱导的规范势和超球上的几何动量) 被Annals of Physics接受发表。两轮审稿，一共六份审稿意见，评价都算很高。审稿意见全录在第三部分。

**一，几何动量十周年**

今年是正式提出几何动量十周年。基本框架已经基本完成，基础性问题已经大体解决。不过，应用性问题基本没有涉及。剩下还有一些重要理论课题包括：轨道自旋耦合，自旋-曲率耦合，拓扑的几何动量效应等等。十余年来，培养了十余位研究生，一共拿了四项国家基金，获得了一项省级科技进步奖。随着一位研究几何动量的博士研究生今年夏天毕业，研究几何动量的步伐，正式进入倒计时。还有一位来自巴基斯坦的博士后专门过来希望学习几何动量，即使如此，我今后参与的几何动量的文章，应该不会超过5篇。

这位巴基斯坦博士，是巴国一所大学的助理教授，2019年秋已经获准进站。但是，他希望带太太和(三个)孩子进入中国，办来办去，疫情起来了，边境严控。两年过去，他居然初心不改，今年秋天终于可以进站了。如果按原来的节奏，已经到了出站时间。天有不测风云。

**二，几何动量两个得意的新引用**

一个来自大师Jacobson, Theodore，Distinguished Univ Professor，University of Maryland, College Park，五月份的如下文章

Particle on the sphere: group-theoretic quantization in the presence of a magnetic monopole

引用了多篇几何动量的文章。

一个来自教学领域的顶级刊物American Journal of Physics 上四月份的论文

Two-body bound states through Yukawa forces and perspectives on hydrogen and deuterium

引用的是：Q. H. Liu and S. F. Xiao, “A self-adjoint decomposition of the radial momentum operator,” Int. J. Geometric Methods Mod. Phys. 12, 1550028 (2015). 这篇论文给狄拉克关于径向动量可观测性这一极具争议性问题一点意见。不过，我们的小文章应该具有定海神针的意义。真怕明珠暗投！

**三，几何动量最新论文的两轮审稿共六份审稿意见**

接收函及六份审稿意见。

Date: Jul 18, 2021

To: "Q. H. LIU"

From: "Annals of Physics" aop@elsevier.com

Subject: AOP 76709R1 accepted

Ms. AOP 76709R1

Title: The curvature-induced gauge potential and the geometric momentum for a particle on a hypersphere

Corresponding Author: Professor Q. H. LIU

Annals of Physics

Dear Dr. LIU:

I am pleased to accept your manuscript, referenced above, for publication.

Please note that your paper will now be sent to the production office for further processing. If you have any questions during this next stage, please contact me at (aop@elsevier.com).

Thank you for submitting your work to Annals of Physics.

Yours sincerely,

Dr. Justin Khoury

Co-Editor

Annals of Physics

--------------------

第二轮审稿意见

Reviewer #1: The authors have improved the discussion concerned the impact of their fidings and I now recommend their manuscript to be published at AOP.

Reviewer #2: The authors have done a good job in the revision. Now I recommend the article for publication.

Reviewer #3: I still believe that the paper should discuss in more depth the issues I raised in the first report. Nonetheless, the answers provided are satisfactory. The paper can now be published, in my opinion.

第一轮审稿意见

**Reviewer #1:** The manuscript deals with an important aspect for a particle constrained on an (N − 1)-dimensional hypersphere: a proper angular momentum algebra. In short, the authors show that it must take into account both the orbital angular momentum and the spin-curvature coupling, in contrast to previous works in the field. **Themanuscript is sound and I recommend publication **once the authors have revised their manuscript in accordance with the following comment:

1- The conclusions cannot be a brief description of what the Authors were done theoretically in the previous sections. The impact of their findings have to be well discussed and possible physical applications should be shortly discussed there.

After this implementation, I believe the manuscript will be more appealing to a general audience.

-----

**Reviewer #2**: The article investigates quantization of the motion of a particle confined to a hypersphere in N-dimensional Euclidean space. The subject is interesting and the paper complements previous results of the literature. The calculations seem to becorrect and the main result makes physical sense. T**he article may be accepted for publication** after some revision. I think it would be educative that the authors include a comment on the N=3 case. My main recommendation concerns the use of the English language. A major revision of grammar and spelling is mandatory.

----

**Reviewer #3**: This paper deals with an interesting and timely topic, even though it is a basic one, hence something one would like to have well under control and understood. And that is precisely my concern here.

**I mean that the paper might be worth publishing** only if it adds clarity to this basic topic. Henceforth, the authors (besidesbeing much more careful with a somehow sloppy English...) have to make an extra effort to:

- discuss in all details how this approach relates to the standard covariant derivative in the presence of spin, because, after all, their Pi_i is a standard derivative, and their p_i is a covariant derivative, henceforth...

- ... they have to show what is the link between their 'gauge field' and the standard spin connection that appears when dealing with fields with spin.

- Furthermore, it is well known in classical field theory, that it is precisely the procedure of imposing constraints that leads to the very same idea of gauge fields. Now, perhaps the authors, or some of them, have already discussed that in some of their previous papers, reported in the Reference. Nonetheless, for completeness of the discussion, to comply with the style and scope of Annals of Physics (that is not a letter journal), and since they claim to be amending text books (like their refs [33] and [34]), a substantial and detailed discussion of this and other general points, is sorely missing...

- ... indeed, they should also fully clarify that the procedure here is made of two separate steps, one for spinless and one for 'spinfull' quantities, and that the literature is, perhaps, not so careful in presenting the issue, but surely this is not entirely missed by those authors.

Overall, at the classical level one indeed has the spin connection already, and that is the classical gauge field that takes care of the spin. One then needs to be careful in defining the proper momenta to be quantized, and this paper comes in hand, also because it is linking that to the quantization in a constrained system, and these days (see, eg., graphene physics) it is nice to have control of that. On the other hand, especially on matters that are well established and discussed in text-books, one needs to be crystal clear, refer to all known results, and explain every single step and the context very clearly. The latter is missing in the present version.

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**接下来干什么？研究小系统热力学。****这方面，前天钱纮教授给了一个年度演讲，值得推荐！**

https://www.koushare.com/lives/room/288344

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