尤金·维格纳Eugene Paul Wigner

尤金·维格纳名字的匈牙利语形式是Jenó Pál 维格纳。他的父亲Antal 维格纳是一家皮革制革厂的厂长，而他的母亲Erzsébet 维格纳照顾三个孩子的家庭。Antal和Erzsébet都来自犹太背景，但他们不 practicing Judaism。维格纳出生在佩斯，这是与布达一起构成匈牙利首都布达佩斯的两个城镇中最东边的一个。他是父母三个孩子中的中间一个，有一个姐姐和一个妹妹。

从五岁起，维格纳就在家里接受私人辅导。十岁时，他进入一所小学，但在学校开始学习大约一年后，他被告知患有肺结核。治疗方法是将他送到奥地利布赖滕施泰因的一家疗养院，他在那里待了六周，然后被告知诊断有误，他从未患过肺结核。然而，这六周的一个好处是，他开始思考数学问题[13]：-

我不得不连续几天躺在躺椅上，我非常努力地研究如果给定三条高，如何构造一个三角形。

1915年，维格纳进入布达佩斯的路德会高中。在这里，他遇到了比他低一年级的冯·诺伊曼。然而，他写道[8]：-

在文理中学，我从不觉得我很了解冯·诺伊曼。也许没有人了解；他总是有点疏离。

这所学校为维格纳提供了数学、文学、古典学和宗教方面的扎实教育。它确实提供了科学教学，但与其他科目相比，这方面的重视程度较低。1919年3月共产党在匈牙利掌权时，他还在中学，整个维格纳家族逃离了这个国家。他们住在奥地利，直到1919年11月共产党被推翻，他们才回到布达佩斯，维格纳完成了他的学校教育。在他十几岁后期，整个维格纳家族皈依了路德宗，但这对维格纳来说意义不大，他后来形容自己“只是温和地信教”。

1920年，维格纳离开学校，是班上最优秀的学生之一。他已经知道数学和物理是适合他的主题，但他意识到冯·诺伊曼[8]：-

……是比我好得多的数学家和更好的科学家。但我懂更多物理。

维格纳想成为一名物理学家，但他的父亲期望他加入家族企业，并且他认为化学工程学位对儿子在家族的皮革制革厂会有用。维格纳遵从了父亲的意愿，攻读了化学工程的第一学位，在布达佩斯的技术学院学习了一年，然后转到柏林的技术高等学校。他说[13]：-

我几乎没去上课……但在实验室里非常努力。我喜欢无机化学。

尽管维格纳攻读的是化学工程学位，但他利用自己的时间学习数学和物理。他与阿尔伯特·爱因斯坦、马克斯·普朗克、冯·劳厄和能斯特一起参加了柏林大学的讨论会。维格纳于1925年在柏林工业大学获得工程博士学位，学位论文为Bildung und Zerfall von Molekülen Ⓣ（分子的形成与分解），导师是迈克尔·波拉尼，他也是来自布达佩斯的同乡。维格纳的学位论文包含了第一个关于分子缔合和解离速率的理论。维格纳和波拉尼于1925年发表了关于这项工作的联合论文。

完成博士学位后，维格纳按计划回到布达佩斯，加入他父亲的制革公司。然而，事情进展得并不太顺利[13]：-

我在制革厂里过得不太好。……我在那里感觉不自在。……我觉得这不是我的生活。……[1926年]我收到威廉皇帝研究所一位晶体学家的来信，[他]想要一名助手……来弄清楚为什么原子在晶格中占据对应于对称轴的位置。……他还告诉我，这与group theory有关，我应该读一本关于群论的书，然后把它弄明白并告诉他。

维格纳的父亲支持他接受柏林的职位。在那里，他阅读了维尔纳·海森堡的论文，但在发展自己的想法时，他意识到数学上存在问题。他于1926年11月12日向Zeitschrift für Physik提交了一篇关于3电子原子光谱的论文，推广了维尔纳·海森堡关于2电子的结果。论文结尾，维格纳写道，他的方法对于超过三个电子的原子来说会复杂得难以承受。然而，他向冯·诺伊曼请教数学上的困难，并被告知去阅读伊赛·舒尔论文中关于群特征标理论的内容。

维格纳由于对晶体的兴趣，已经读过海因里希·马丁·韦伯的Lehrbuch der AlgebraⓉ（代数教科书），并且已经从韦伯的教材中获得了矩阵方面的专业知识，他发现伊赛·舒尔的论文很容易理解。他还研究了由费迪南德·格奥尔格·弗罗贝尼乌斯和威廉·伯恩赛德提出的对称群的表示论。正如冯·诺伊曼所建议的，这个理论正是他发展具有$n$电子的原子光谱理论所需要的。然后他开始了他著名的工作，即将群论应用于量子力学。他关于$n$电子情况的论文于1926年11月26日提交给Zeitschrift für Physik。

维格纳于1927年受邀前往哥廷根，成为大卫·希尔伯特的助手。大卫·希尔伯特已经对量子力学感兴趣，觉得需要一位物理学家作为助手来补充自己的专长。这对维格纳来说是一个重要时期，他发表了具有重大深度和意义的论文，在On the conservation laws of quantum mechanics（1927）一文中引入了宇称的新概念。然而，他与大卫·希尔伯特的合作不太成功，因为他们一年中只见过五次面[8]：-

我发现他极度孤僻。……他巨大的疲惫显而易见。

维格纳在哥廷根待了一年后回到柏林，在那里讲授量子力学，撰写他的著名著作Group theory and its application to the quantum mechanics of atomic spectra，并继续他的研究。事实上，维格纳关于群论在量子力学中应用的著作并非最早问世的，因为赫尔曼·外尔比维格纳稍早出版了他的著作。然而，正如Mackey在[3]中所写：-

赫尔曼·外尔的想法与维格纳的不同之处在于，他想应用群表示来更好地理解量子力学的一般基础，而不是为了深入了解具体问题。

一份去普林斯顿待一学期的邀请使他在1930年底前往美国。从1930年到1933年，维格纳每年有一部分时间在普林斯顿，一部分时间在柏林。他的柏林职位随着1933年通过的纳粹规定而消失，此后，除了1936年至1938年在威斯康星之外，维格纳的余下职业生涯都在普林斯顿度过。1934年，他的妹妹Margit（一直被称为Manci）来到普林斯顿与哥哥团聚。在那里她遇到了来访的保罗·狄拉克，两人于1937年1月结婚。

关于维格纳1936年离开普林斯顿的原因，存在一些混淆。在[8]中他说：-

1936年来了一个打击……普林斯顿解雇了我……他们从未解释原因……我不禁感到愤怒。

然而，Pais在[16]中指出，维格纳的这一说法并不严格准确，他并没有被解雇。相反，看来是他在普林斯顿没有得到他认为自己应得的晋升，于是请假去威斯康星接受了一个代理教授的职位。在威斯康星期间，维格纳成为了美国公民。同样在威斯康星大学麦迪逊分校期间，他遇到了Amelia Frank并与之结婚。她是那里的一名物理学生，但幸福很快被巨大的痛苦所取代，因为她患上了癌症，并在结婚不到一年后的1937年去世。

在威斯康星期间，维格纳展示了特殊酉群SU(4)在考虑核力时的作用，并构造了亨德里克·洛伦兹群的一类不可约酉表示。Kim在[12]中写道：-

维格纳1939年关于非齐次亨德里克·洛伦兹群表示的论文[Ann. of Math. (2) 40 (1939), 149-204]是物理学中最基础的论文之一。

1938年，他被任命为普林斯顿大学托马斯·D·琼斯数学物理讲席教授。1939年，他将父母接到美国。起初他们住在普林斯顿，后来搬到纽约州一个更乡村的地方。他们在美国从未感到快乐，就此而言，维格纳也从未真正感到自在。在他生命接近尾声时，他写道：-

在美国生活60年后，我仍然更像匈牙利人而非美国人。……美国文化的许多方面我无法理解。

1940年，他遇到了来自瓦萨学院的物理教师玛丽·安妮特·安娜·约翰逊·佩尔·惠勒，他们于1941年6月4日结婚。他们有两个孩子：David Wigner，在乔治·伯克利的加利福尼亚大学教数学；以及玛莎，在芝加哥地区从事交通系统工作。

第二次世界大战期间，从1942年到1945年，维格纳在芝加哥大学参与曼哈顿计划。他的工程师训练为他关于核裂变的战时工作提供了宝贵的背景。

维格纳于1963年获得诺贝尔物理学奖。I·沃勒的颁奖演讲将维格纳的贡献置于其背景中：-

为了能够计算核子的运动，还必须知道它们之间作用的力。维格纳在1933年对这些力的研究迈出了非常重要的一步，他从一些实验中推断出，两个核子之间的力非常弱，除非它们之间的距离非常小，但那时这个力比原子外层电子之间的电力强一百万倍。维格纳后来发现了核力的其他重要性质。

……根本重要的是，维格纳能够表明原子核的最本质属性源于运动定律中普遍成立的对称性。早先，维格纳通过研究电子运动定律中的这类对称性做了开创性工作，并通过考察例如那些表达如下事实的对称性——即上述定律不区分左右，且按这些定律时间向后与时间向前等价——而有了重要发现。这些研究在20世纪30年代末被维格纳推广到原子核，他当时还探究了新发现的核子间作用力的对称性质，即无论哪个核子是质子还是中子，这种力都相同。维格纳的这项工作以及他对物理学中对称原理的其他研究，其重要性远远超出核物理本身。他的方法和结果已成为解读近年来基本粒子实验研究中所呈现的丰富而复杂图景的不可或缺的指南。它们也为更深入地渗透并部分修正此前关于左右对称的概念做了重要的准备……

维格纳对核物理学做出了许多其他重要贡献。他给出了核反应的一般理论，并对核能的实际应用做出了决定性贡献。他常常与年轻科学家合作，在物理学的许多其他领域开辟了新路径。

R L Ingraham总结了维格纳做出的许多贡献中的一些。这些包括他的：-

... 关于对称性如何在量子力学中实现的划时代工作，儒勒·昂利·庞加莱群的所有不可约酉表示的确定，以及他与Bargmann合作将这些不可约酉表示实现为相对论性波动方程解的大卫·希尔伯特空间的工作，... 量子力学中的离散对称性和超选择规则，对称性对原子和分子光谱的蕴含，自然线宽理论，微观物理学与宏观物理学以及广义相对论与量子力学的对比，解释为什么对称性对量子力学比经典力学产生更多信息，哲学问题如自然定律应该是什么，因果性的限制，以及量子力学原则上能否解释生命。

他的重要著作包括与L 大卫·艾森布德合著的Nuclear Structure（1958），与A Weinberg合著的The Physical Theory of Neutron Chain Reactors（1958），Dispersion Relations and Their Connection with Causality（1964），以及Symmetries and Reflections（1967）。他1960年关于The Unreasonable Effectiveness of Mathematics的论文引发了关于数学在科学中作用的广泛辩论。

维格纳因其杰出工作获得了许多荣誉。他于1946年被授予美国功绩勋章，1958年获恩里科·费米奖，1960年获原子用于和平奖、富兰克林学会奖章、德国物理学会的马克斯·普朗克奖章、美匈研究基金会的乔治·华盛顿奖（1964）、美匈医学协会的塞梅尔魏斯奖章（1965）以及国家科学奖章（1969）。授予他荣誉学位的大学名单很长，包括威斯康星大学、华盛顿大学、凯斯理工学院、阿尔伯塔大学、芝加哥大学、科尔比学院、宾夕法尼亚大学、叶史瓦大学、蒂尔学院、圣母大学、柏林工业大学、斯沃斯莫尔学院、鲁汶大学、列日大学、伊利诺伊大学、天主教大学和洛克菲勒大学。他于1970年当选为伦敦皇家学会会士，其他学术团体成员身份包括国家科学院、American Academy of Arts and Sciences、Royal Netherlands Academy of Sciences and Letters、美国科学促进会、Austrian Academy of Sciences以及哥廷根的Gesellschaft der Wissenschaften。

A J Coleman写道：-

……维格纳关于高等量子力学的课程，我有幸于1940年在普林斯顿听过。我记得他思维敏锐如刀，性情温和善良。

许多其他关于维格纳个性的提及都让人感到，尽管有诸如[8]和[13]这样广泛的访谈，他仍然是一个略显神秘的人。正如16中Pais所写：-

他是一个非常奇怪的人，也是二十世纪物理学的巨人之一。

也许我们应该以维格纳自己的话作为结束：-

未来科学的承诺是为人类提供一个统一的目标，而不仅仅是过安逸生活的手段，是在面包之外提供人类灵魂所需的一些东西。

The Hungarian version of Eugene Paul Wigner's name was Jenó Pál Wigner. His father, Antal Wigner, was the director of a leather-tanning factory while his mother, Erzsébet Wigner, looked after the family of three children. Both Antal and Erzsébet were from a Jewish background but they did not practice Judaism. Paul was born in Pest, the eastmost of the two towns which, together with Buda, formed the Hungarian capital of Budapest. He was the middle of his parents three children, having both an older and younger sister.

From the time he was five years old Wigner was given private tuition at home. When he was ten years old he entered an elementary school but about a year after he began his studies at the school he was told that he had tuberculosis. The cure was to be found in sending him to a sanatorium in Breitenstein in Austria and he spent six weeks there before being told that the diagnosis had been wrong and that he had never had tuberculosis. However, one advantage of his six weeks was that he began to think about mathematical problems [13]:-

I had to lie on a deck chair for days on end, and I worked terribly hard on constructing a triangle if the three altitudes are given.

In 1915 Wigner entered the Lutheran High School in Budapest. Here he met John von Neumann who was in the class below him. However he wrote [8]:-

I never felt I knew von Neumann well at Gymnasium. Perhaps no one did; he always kept a bit apart.

The school provided a solid education for Wigner in mathematics, literature, classics and religion. It did provide science teaching, but there was less emphasis on this than on other subjects. He was still at the Gymnasium when the communists took control in Hungary in March 1919 and the whole Wigner family fled the country. They lived in Austria until the communists were overthrown in November 1919 when they returned to Budapest and Wigner completed has school education. When he was in his late teens the whole Wigner family became converts to Lutheranism but it did not mean a great deal to Wigner who in later life described himself as "only mildly religious".

In 1920 Wigner left school being one of the top students in his class. Already he knew that mathematics and physics were the topics for him but he realised that von Neumann [8]:-

... was a much better mathematician than I was and a better scientist. But I knew more physics.

Wigner wanted to be a physicist but his father expected him to join the family business and he believed that a degree in chemical engineering would be useful to his son in the family's leather-tanning factory. Wigner followed his father's wishes and took his first degree in chemical engineering spending one year at the Technical Institute in Budapest, then moving to the Technische Hochschule in Berlin. He said [13]:-

I went to practically no classes ... but worked extremely hard in the laboratory. I loved inorganic chemistry.

Despite working for a degree in chemical engineering, Wigner studied mathematics and physics in his own time. He attended colloquia at the University of Berlin with Einstein, Planck, von Laue, and Nernst. Wigner obtained the degree of Dr. Ing. in 1925 from the Technische Hochschule in Berlin with a thesis Bildung und Zerfall von Molekülen Ⓣ supervised by Michael Polanyi, who was a fellow countryman also from Budapest. Wigner's thesis contains the first theory of the rates of association and dissociation of molecules. Wigner and Polanyi published a joint paper on this work in 1925.

Having completed his doctorate, Wigner returned to Budapest to join his father's tannery firm as planned. However, things did not go too well [13]:-

I did not get along very well in the tannery. ... I did not feel at home there. ... I did not feel that this was my life. ... [In 1926] I received a letter from a crystallographer at the Kaiser Wilhelm Institute [who] wanted an assistant ... to find out why the atoms occupy positions in the crystal lattices which correspond to symmetry axes. ... He also told me that this had to do with group theory and that I should read a book on group theory and then work it out and tell him.

Wigner's father supported him taking the post in Berlin. There he read Heisenberg's papers but in developing his own ideas he realised that the mathematics presented problems. He submitted a paper on the spectrum of atoms with 3 electrons to Zeitschrift für Physik on 12 November 1926 extending Heisenberg's results for 2 electrons. The paper ends with Wigner writing that his methods would be prohibitively complicated for atoms with more than three electrons. However, he asked von Neumann for advice on the mathematical difficulties and was told to read about the theory of group characters in Schur's papers.

Wigner, because of his interest in crystals, had already read Heinrich Weber's Lehrbuch der Algebra Ⓣ and, already having an expertise in matrices from Weber's text, he found Schur's papers easy to understand. He also studied the representation theory of the symmetric group due to Frobenius and Burnside. The theory, as von Neumann suggested, was exactly what he needed to develop a theory of the spectrum of atoms with $n$ electrons. He then began the work for which he is famous, namely applying group theory to quantum mechanics. His paper on the case of $n$ electrons was submitted to the Zeitschrift für Physik on 26 November 1926.

Wigner was invited to Göttingen in 1927 to become Hilbert's assistant. Hilbert, already interested in quantum mechanics, felt that he needed a physicist as an assistant to complement his own expertise. This was an important time for Wigner who produced papers of great depth and significance, introducing in his paper On the conservation laws of quantum mechanics (1927) the new concept of parity. However his collaboration with Hilbert was less successful for they only met five times during the year [8]:-

I found him painfully withdrawn. ... His enormous fatigue was plain.

Wigner returned to Berlin after the year in Göttingen where he lectured on quantum mechanics, worked on writing his famous text Group theory and its application to the quantum mechanics of atomic spectra and continued his research. In fact Wigner's book on the applications of group theory to quantum mechanics was not the first to appear, since Weyl published his a little before Wigner. However, as Mackey writes in [3]:-

Weyl's ideas differed from those of Wigner in that he wanted to apply group representations to get a better understanding of the foundations of quantum mechanics in general and not so much to gain insight into particular problems.

An offer to spend a term in Princeton saw him travel to the United States at the end of 1930. From 1930 to 1933 Wigner spent part of the year at Princeton, part at Berlin. His Berlin post vanished under the Nazi rules passed in 1933 and from then, except for the years 1936 - 1938 in Wisconsin, Wigner spent the rest of his career at Princeton. In 1934 his younger sister Margit (always known as Manci) joined her brother in Princeton. There she met Dirac, who was a visitor, and the two married in January 1937.

There is slight confusion about the reason that Wigner left Princeton in 1936. In [8] he said:-

In 1936 came a shock ... Princeton dismissed me ... they never explained why ... I could not help feeling angry.

Pais points out in [16] however, that this statement by Wigner is not strictly accurate and he was not dismissed. Rather it appears that he was not receiving the promotion in Princeton which he felt that he deserved and so took leave of absence to accept a position of acting professor in Wisconsin. While in Wisconsin, Wigner became a U.S. citizen. Also while at the University of Wisconsin at Madison he met and married Amelia Frank. She was a physics student there but the happiness was soon replaced by much pain for she fell ill with cancer and died in 1937 less than a year after the marriage.

While in Wisconsin Wigner showed the role of the special unitary group SU(4) in considering nuclear forces and he constructed a class of irreducible unitary representations of the Lorentz group. Kim writes in [12]:-

Wigner's 1939 paper on representations of the inhomogeneous Lorentz group [Ann. of Math. (2) 40 (1939), 149-204] is one of the most fundamental papers in physics.

He was appointed to the Thomas D Jones Chair of Mathematical Physics at Princeton in 1938. He brought his parents to the United States in 1939. First they lived in Princeton, then they moved to a more country place in New York State. They were never happy in the United States and for that matter Wigner never really felt at home. Near the end of his life he wrote:-

After 60 years in the United States I am still more Hungarian than American. ... much of American culture escapes me.

He met Mary Annette Wheeler, a physics teacher from Vassar College, in 1940 and they were married on 4 June 1941. They had two children, David Wigner who taught mathematics at the University of California in Berkeley, and Martha who worked on the transportation system in the Chicago area.

Wigner worked on the Manhattan Project at the University of Chicago during World War II, from 1942 to 1945. His training as an engineer proved valuable background for his war work on nuclear fission.

Wigner received the Nobel Prize for Physics in 1963. The presentation Speech by I Waller put Wigner's contributions into their context:-

In order to be able to calculate the motion of the nucleons it was ... necessary to know also the forces which act between them. A very important step in the investigation of these forces was taken by Wigner in 1933 when he found, deducing from some experiments, that the force between two nucleons is very weak except when their distance apart is very small but that the force is then a million times stronger than the electric forces between the electrons in the outer part of the atoms. Wigner discovered later other important properties of the nuclear forces.

... It was ... fundamentally important that Wigner could show that most essential properties of the nuclei follow from generally valid symmetries of the laws of motion. Earlier Wigner had performed pioneering work by studying such symmetries in the laws of motion for the electrons and had made important discoveries by investigating e.g. those symmetries which express the fact that the laws mentioned make no difference between left and right and that backward in time according to them is equivalent to forward in time. These investigations were extended by Wigner to the atomic nuclei at the end of the 1930s and he explored then also the newly discovered symmetry property of the force between two nucleons to be the same whether either of the nucleons is a proton or a neutron. This work by Wigner and his other investigations of the symmetry principles in physics are important far beyond nuclear physics proper. His methods and results have become an indispensable guide for the interpretation of the rich and complicated picture which has emerged from recent years' experimental research on elementary particles. They were also an important preliminary for the deeper penetration into and the partial revision of the earlier concepts concerning the right-left symmetry ...

Wigner has made many other important contributions to nuclear physics. He has given a general theory of nuclear reactions and has made decisive contributions to the practical use of nuclear energy. He has, often in collaboration with younger scientists, broken new paths in many other domains of physics.

R L Ingraham summarised some of the many contributions made by Wigner. These include his:-

... epoch-making work on how symmetry is implemented in quantum mechanics, the determination of all the irreducible unitary representations of the Poincaré group, and his work with Bargmann on realizing those irreducible unitary representations as the Hilbert spaces of solutions of relativistic wave equations, ... discrete symmetries and superselection rules in quantum mechanics, symmetry implications for atomic and molecular spectra, natural line-width theory, contrast of microscopic and macroscopic physics and of general relativity and quantum mechanics, explanation of why symmetry yields more information for quantum than for classical mechanics, philosophical questions such as what nature laws should be, limits on causality, and whether quantum mechanics could in principle explain life.

His important works include Nuclear Structure (1958) with L Eisenbud, The Physical Theory of Neutron Chain Reactors (1958) with A Weinberg, Dispersion Relations and Their Connection with Causality (1964), and Symmetries and Reflections (1967). His 1960 paper on The Unreasonable Effectiveness of Mathematics has provoked a wide debate on the role of mathematics in science.

Wigner received many honours for his outstanding work. He was awarded the United States Medal for Merit in 1946, the Enrico Fermi Prize in 1958, and the Atoms for Peace Award in 1960, the Medal of the Franklin Society, the Max Planck Medal of the German Physical Society, the George Washington Award of the American-Hungarian Studies Foundation (1964), the Semmelweiss Medal of the American-Hungarian Medical Association (1965), and the National Medal of Science (1969). The list of universities which awarded him an honorary degree is extensive, University of Wisconsin, Washington University, Case Institute, University of Alberta, University of Chicago, Colby College, University of Pennsylvania, Yeshiva University, Thiel College, Notre Dame University, Technische Universität Berlin, Swarthmore College, Université de Louvain, Université de Liège, University of Illinois, Catholic University, and The Rockefeller University. He was elected a Fellow of the Royal Society of London in 1970 and other memberships of learned societies included the National Academy of Science, the American Academy of Arts and Sciences, the Royal Netherlands Academy of Sciences and Letters, the American Association for the Advancement of Science, the Austrian Academy of Sciences, and the Gesellschaft der Wissenschaften of Göttingen.

A J Coleman writes of the:-

... course by Wigner on advanced quantum mechanics which I had the good fortune to attend at Princeton in 1940. I recall a person with razor-sharp mind and of a kind and gentle spirit.

Many other references to Wigner's personality leave the feeling that, despite the extensive interviews such as [8] and [13], he is still someone who is slightly mysterious. As Pais writes in [16]:-

He was a very strange man and one of the giants of twentieth-century physics.

Perhaps we should end with Wigner's own words:-

The promise of future science is to furnish a unifying goal to mankind rather than merely the means to an easy life, to provide some of what the human soul needs in addition to bread alone.