一，理论物理好玩不好玩?

多年前杨振宁先生就呼吁国家应当重视应用研究，现在连Phys. Rev.都准备出版Applied分卷。看来，基础部分的研究要让出越来越多的位置。我校一个应用物理类的研究所，今年一口气就斩获了10项国家自科基金。单就一本Advanced Materials (影响因子(IF) 14.8)，去年他们出了一篇特邀文章，今年似乎出了一篇封面文章，明年也许更热闹。就影响因子而言，应用物理类、材料学类许多刊物轻松打倒Phys. Rev. Lett.(IF 7.9)。不过呢，物理学类很多刊物还能轻松打倒J. Am. Math. Soc. (IF 3.6)，而数学类很多刊物还能轻松打倒最好的哲学刊物呢。

国际上，理论物理的主流刊物没有变化，队伍规模也基本没有大的改变。就一亩三分薄田，耕种还是老一套：提出一个理论，确认它有本质上不同的实验或者观测预言，确立它在理论物理版图中的一个角落。和科学的蓬勃发展和学科加速分化相比，理论物理似乎还在罗马斗兽场阶段。为什么理论物理研究还有吸引力?  因为它实在是好玩!

理论物理领域不认权威，没有教条。只要对这个宇宙间的事情提供一丁点的深入理解，任何在这个领域内工作的人士，都拥有绝对思想自由的权利。

这就是理论物理的好玩之处。

一个好玩处，就有万般好玩事。

今天只说一件。

二，如何看待几何动量?

几何动量实在是个丰饶的小方向，可以做很多事情，养活一个小课题组不成问题。今年做了一些事情，完成了若干论文，其中有两篇刚刚接受，就说这两篇。

一篇处理了超曲面上的粒子的量子力学。探讨了几何动量和几何能量有何有趣性质，结果暗示和暗能量的可能关系。刚刚被J. Math. Phys. 接受。

另一篇发现，基于内禀几何的理论(例如广义相对论)本质上不能和量子力学自洽。刚刚被Ann Phys (NY) 接受。

这两篇文章都够大胆。

先说Geometric momentum for a particle constrained on a curved hypersurface。这篇文章也是对温老一个错误的终极解决。故事参见：赢了温伯格先生一本签名赠书。

为了获得对这个问题的完全解，先给出了一个理论假设，然后看具体看超球嵌入高维平直空间，然后看附加的能量对空间维数的依赖。发现，四维以上这个附加的能量为正，这和暗能量至少符号上相合。于是，文章最后一句话是： There are interesting issues which will be explored in near future: …, and the possible influence of the geometric potentialon the dark energy as a consequence of embedding our universe in higher dimensional flat space-time, etc.

这篇文章被J. Math. Phys.直接接受发表，12月接受，明年1月刊行。在文章寄出之时，同时放在在预印本库中，在中外许多场合报告过。

全部审稿意见如下：

Editor's Recommendation: Publish as is

Associate Editor Recommendation: Publish as is

Referee Recommendation: Publish as is

Referee #1(Comments to the Author):

The paper is devoted to quantisation of particle motion constrained to a spherical surface. Quantizing such constrained models is a complicated problem with various non- unique answers in the literature. The author pursues his own idea whichamounts to taking more commutation relations into account when going from agiven classical formulation to the quantum one. I think that this is a veryinteresting subject, and the paper presents some novel results. I would onlyremark that XXX(删除几个字). But otherwise I certainly recommend this paper forpublication in its current form.

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再说第二篇Can Diracquantization of constrained systems be fulfilled within the intrinsic geometry?

今年已经在Ann Phys(NY)发表的一篇文章，还上了一个排行版。又送去这篇，11月26日通知接受，12月12日就正式online了, 明年2月出纸质版。

审稿人实在是小同行，一眼就看出了要害。并建议说，要把这要害突出，给出一个例证就可以了，两个就累赘了，删去一个。题目要更有力，要直接瞄准Dirac而去。

他给出的全部意见如下(也是具有建设性的审稿意见的样板)：

The observations of the paper are relevant to the theory of quantization of constrained systems and in my opinion should be publishedin Annals of Physics. However, prior the publication theauthors should make the following amendments.

1) Referring to the question posed in the title, it is clearthat the purpose of the paper is to provide a counterexample showing thatwithin the Dirac theory the description of the motion based on the treatment ofa configuration space as a submanifold of the Euclidean space is moreappropriate than examination of the motion in terms of the intrinsic geometry. Thenegative answer to the question posed in the title is clearly justified by the(counter)example of the helicoid and I see no reason for the detaileddiscussion of the case of the catenoid, all the more, it contains asremarked by the authors, some problematic points. Therefore, in my opinion thecase of the catenoid should only be briefly mentioned.

2) Thechoice of surfaces with zero mean curvature (minimal surfaces) as an object ofthe study should be better motivated.  

3) Insection "Quantum mechanical treatment" the authors should provide theconcrete form of the Hilbert space of square integrable functions on a helicoidand discuss at least hermiticity (symmetry) of the momentum operators(119)--(121). Of course, the proof of the self-adjointness would be even better.  

4) The title of the paper should be changed from "Canproper canonical quantization be fulfilled within the intrinsic geometry" to"Can Dirac quantization of constrained systems be fulfilled within theintrinsic geometry" Theusage of the term "proper quantization" suggests that there are noalternatives of the Dirac approach, which is obviously not the case. Forinstance, such important results related to quantum mechanics on a sphere asanalysis of the quantum rotator which can be found in most textbooks orconstruction of coherent states were obtained without usage of the Diracquantization.  

5) Bearingin mind 4) and the fact that the authors discussed merely two particularexamples of minimal surfaces, the statement from the section "Discussionsand conclusions": "We can safely conclude that the intrinsic geometrydoes not offer in general a framework for quantum mechanics to besatisfactorily formulated" should be reformulated in less categoricalform.

三，国际理论物理学界对新东西很宽容

从2011年Phys. Rev.A接纳几何动量这个量子力学概念开始，用几何动量作为题目在美欧主流理论物理刊物发表了接近10篇论文。几乎没有阻力。

国际理论物理学界对新东西真是很宽容。