介紹一位「平凡的」華人物理學家——馬上庚

最近在學習一些關於自旋玻璃（spin glass）的理論工作，需要用到重正化群的方法，於是鑽研《臨界現象的現代理論》一書。原本並沒有太注意到這位作者，直到讀論文，從最新的進展一直追溯到1975年的文獻，發現其中一篇文章的作者正是這位S.K. Ma。並且遺憾的發現，這些40多年前的工作，我還是很難讀懂......帶著崇敬的心情，我查找了一下馬上庚教授的生平簡介，卻發現幾乎鮮有中文的介紹，在國外網站上才找到一些簡單的記述。

馬上庚教授生於抗戰時期，後赴美留學，主要研究多體理論。在UCSD成為教授之後，他在重正化理論等方向作出了開創性的貢獻。可惜在43歲便英年早逝。

令人欣慰的是，在重正化群理論這樣一個重要的工作中，留下了一位中國人的名字。他像一顆不那麼閃亮的流星，匆匆划過無邊無際的物理世界。但是在50年、甚至更久之後，依然能有學生，經過幾十篇文章的索引，來到一個早已作古的名字前，去請教一個小小的問題。當一位普通的中國小博士生在卷帙浩繁的文獻中求索，在無數外國的雜誌、外國的學者間，看到一個屬於亞洲人、中國人的名字，多少能感到一些慰籍。

遺憾的是在網上幾乎沒能找到關於馬上庚教授的介紹，除了以下這篇悼詞。這篇文章也是《Directions in Condensed Matter Physics》一書的序，此書為該系列中的馬上庚紀念刊。書中收錄了部分該領域知名研究者的文章，他們都曾和馬上庚有所往來，包括：軟物質之父、諾獎得主P.G. de Gennes，諾獎得主A. Leggett，以及A. Aharony, J. Langer等該領域的重要人物。足見當時馬上庚的學術地位。

Memories of Shang-keng Ma

紀念馬上庚教授

Our text, An Introduction to Computer Simulation Methods, is dedicated to the memory of Shang-keng Ma.

The following is a slightly edited version of a talk given in memory of Shang-keng Ma by Fred Y. Wu at the 50th statistical mechanics meeting at Rutgers University, December 15, 1983.

本文獻給故去的馬上庚教授。

以下是在1983年12月第50屆統計力學會議上，Fred Y.Wu紀念馬上庚教授的發言（略作修訂）。

I speak with great sorrow and deep grief of the loss of our friend, colleague, and coworker, Shang-keng Ma. Shang-keng was born in 1940 in Chungking, the World War II capital of China. He came to this country at the age of eighteen and entered U. C. Berkeley to study physics. He obtained his B. S. degree there in 1962 with the honor of the "most promising senior," and continued on to earn a Ph.D. in 1966 at Berkeley under the direction of Professor Kenneth Watson. His Ph.D. work was in many-body theory, and it was natural that he did his postdoctoral work with Professor Keith Brueckner at U. C. San Diego, where he eventually became a full professor in 1975.

在這裡我沉痛懷念我們的朋友和同事——馬上庚教授。馬上庚生於二戰時的中國重慶，18歲時赴美留學，於U.C.Berkeley主修物理。在1962年獲得「優秀」本科學位，後在K.Watson教授的指導下研究多體理論，於1966年獲博士學位。後來在U.C.San Diego的K.Brueckner教授手下從事博士後工作，最終於1975年獲評該校全職教授。

His early work reflected much of his Ph.D. training. His first publication was with Chia-Wei Woo, who also was a postdoctoral research associate working with Brueckner at the same time. They collaborated on two papers on the charged Bose gas, obtaining the same results using two entirely different approaches, one using Greens functions and the other using correlated basis wave functions. Ma subsequently worked on various problems in different fields, including the electron gas, fermion liquids, and quantum electrodynamics, all with the flavor of Greens functions. During those early years, Chia-Wei once related to me that Shang-keng had confided to him that he could not do anything without Greens functions. But this was soon to change.

他早期與吳家偉（Chia-Wei Woo）合作，研究帶電波色氣體。後來他運用格林函數法，研究電子氣、費米液體、量子電動力學等。在那個時期，家偉曾和我說，上庚自己承認，要是不用格林函數，他幾乎什麼都做不了。後來情況發生了變化。

During the period of 1969-72, Shang-keng continued to work in both condensed matter as well as high energy physics, often bridging the two, producing papers with titles such as "Singularities in Forward Multi-Particle Scattering Amplitudes" and the "S-Matrix Interpretation of Higher Virial Coefficients." In 1972 his interest shifted to the then rapidly emerging area of renormalization group theory. To learn the development first-hand from the originators, he took a leave from La Jolla and spent a few months at Cornell with Ken Wilson and Michael Fisher. Soon thereafter he produced a number of important and influential papers on the subject, among them, the 1/N and 1/n expansions, and the first review article on renormalization group. Since then, he worked in diverse areas of critical phenomena and statistical physics, including critical dynamics of ferromagnet and spin glasses, magnetic chains, and the study of the Boltzmann equation.

在1969年到1972年期間，上庚繼續從事凝聚態和高能物理的相關研究，常常把兩個領域聯繫起來。在1972年，他開始關注當時迅猛發展的重正化群理論。他在Cornell花了數月時間，向該領域最初的幾位創始人，Ken Wilson以及Michael Fisher，習得了第一手的進展，之後便作出了好些重要的工作，比如1/N的展開等，寫出了重正化理論的第一篇綜述。在這之後，他開始在多個領域開展研究，包括鐵磁和自旋玻璃的臨界動力學等。

In 1976 Shang-keng introduced the idea of Monte Carlo renormalization group, an approach that has now become fashionable. His most recent contribution with Joseph Imry was on random systems, on the change of the critical dimensionality of spin systems due to the presence of random fields. He also had formulated a new way of considering entropy in dynamical systems. These works are full of physical intuition and new ideas, and are very different from his earlier Greens function calculations. It is clear that Shang-keng was just at the beginning of making an impact in many areas of statistical physics. He visited many institutions to pursue his ideas, including Cornell, the Institute for Advanced Studies at Princeton, Berkeley, Saclay, Harvard, National Tsing Hua University of Taiwan, and the IBM Watson Research Center.

在1976年上庚提出了蒙特卡洛的重正化群方法。最近他和Joseph Imry合作，研究隨機場下的自旋體系，同時建立了研究動力學系統的熵的新方法。這些工作展現了物理的直覺，顯然上庚正要開始在統計物理的各個領域做出自己的影響。

Shang-kengs work is characterized by a unique style of elegance and profound thinking. He was, as Leo Kandanoff remarked to me, a deep thinker, not just a calculator. He wrote two books. His first book Modern Theory of Critical Phenomena, was published by Benjamin and has been translated into Russian. His most recent book Statistical Mechanics was written in Chinese. In this book which was published earlier this year, statistical mechanics is presented in an unconventional way reflecting his unique style and way of thinking. The book was intended to students of all fields and is very readable. Fortunately for readers in the West, it is now available in an English edition.

上庚的工作有著獨特的優雅以及深刻的思考。Leo Kandanoff（卡丹諾夫）曾對我評價道：上庚不是一位計算者，他是深邃的思想者。上庚出版了兩本書，英文版的《臨界現象的現代理論》以及用中文寫成的《統計力學》。

Shang-keng was a dedicated teacher and researcher, and a devoted father and husband. He was also talented in many areas outside physics. His greatest past-time was reading Chinese classics. He was a regular contributor of articles to newspapers and magazines in Taiwan. One of his unfinished works on his desk was a novel on cancer patients written in Chinese. He was a student of oil painting for many years, and he enjoyed and sang Chinese operas and played the ancient Chinese musical instrument "tseng" very well.

上庚是敬業的教師和研究者，也是摯愛的丈夫和父親。在物理之外，他也天賦諸多。他喜歡閱讀中文經典，常常在台灣的報刊雜誌上刊載文章，他的書桌上現在還留著他未完成的遺作，是一部關於患癌病人的小說。他還學習油畫多年，喜歡京戲，還是一位古箏演奏高手。

Although he was not a smoker, Shang-keng was found to have lung cancer in May 1982 shortly after returning home from a sabbatical leave in Taiwan. While he worked hard in Taiwan including finishing his second book, the hard work took an apparent toll since by then it was too late for treatment. Doctors soon gave up on him and he gave up on the doctors in return. In order to lead a normal family life, especially with his children, Shang-keng chose to stay at home and work as usual, despite all the pain he had to suffer. It was a courageous fight from the very beginning. He mentioned on the phone the pain that kept him awake at night, but he did not give up. He continued to teach and do research until two weeks before Thanksgiving, when the doctor brought the worst news after a blood test. But he was confined to bed only in his last four days. The abstract of his last paper "Entropy of Polymer Chains Moving in a Two Dimensional Square Lattice" was finished one week before his death. By that time, he was unable to read and had to rely on Claudia, his wife, to read the text for corrections. He passed away in his home, in the early hours of Thanksgiving Day, leaving Claudia and two sons, Tian-Shan and Tian-Mo, ages three and fifteen months.

在1982年三月，從不吸煙的上庚被發現患有肺癌。那時他正在台灣努力完成他的第二本書，代價顯然是慘重的，因為疾病被發現時已是晚期。醫生放棄了治療，上庚也免去了治療的苦痛。在他最後的日子裡，上庚選擇和家人——尤其是兩個孩子——呆在一起；雖然飽受病痛折磨，他還是照常工作。面對病魔，上庚一直非常勇敢，他曾在電話中說到病痛使他夜夜無眠，但他從未放棄。他仍在繼續教書和研究。在逝世前一周，他完成了他最後的論文；直到逝世前四天，他才被迫卧床休息。那時他無法閱讀，只能靠著太太Claudia念出文字，以供修訂。在感恩節來臨前的幾個小時，他在家中離世，留下了太太Claudia和兩個幼子，三歲的Tian-Shan以及十五個月的Tian-Mo。

Last night I spoke to Claudia and asked her if there was anything that Shang-keng would have wanted to tell us, his friends, colleagues, and coworkers, on this occasion. After a pause, she said that Shang-keng had told her that he would like to be remembered as an ordinary person. Yes, just an ordinary person.

昨晚我問Claudia，上庚有沒有留下什麼話給他的朋友和同事們。她頓了頓，說上庚希望大家記住自己，作為一個平凡的人。是的，只是一個平凡的人。

There is an old Chinese saying which says "the truly greatness is being ordinary." With this quote I would like to close, and hope we all remember our friend and colleague, Shang-keng Ma, as the ordinary person who worked so hard and contributed so much.

有句中國古話說「大音希聲」。我們永遠懷念我們的朋友、同事，馬上庚教授，這位工作勤勉、貢獻良多的平凡的人。