ポール・ディラック
【数々の数学と逸話を生んだケンブリッジの天才】

　伝統を受け継ぐディラック

しかし、そんなディラックは真面目な性格、心を重んじる性格
もあって周囲から大事にされていた様子が伺われます。

本ブログのTOP画面で使っている集合写真でも
真ん中の列の中央に居ます。若き天才ディラックに
アインシュタインやキュリー夫人が気を遣って
「君の研究は素晴らしい。これからも頑張って下さいよ！」
といった気持で尊重しているような気がするのです。

そして、写真の真ん中にニュートンの伝統を受け継ぐ
ケンブリッジで研究をするディラックが居て、共に
時代を重ねていくパウリやハイゼンベルクが居るのです。

そして、
ディラックはイギリスの伝統を受け継いだ人でもあります。
ケンブリッジではルーカス教授職を務めました。

この名誉は初代・アイザック・バローから始まり
二代目・アイザック・ニュートンと続き、ディラックが継ぎ、
最近では宇宙論で名を成したＳ・W・ホーキング博士
が受け継いでいます。

〆
【スポンサーリンク】

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2020/08/17_初稿投稿
2023/08/08_改定投稿
2024/09/03‗改訂投稿

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（2021年10月時点での対応英訳）

Quiet Dirac

Dirac in England was a very humble and reticent person. When the Nobel Prize was decided, he seemed to be thinking about declining the award for fear of becoming famous. Although he is such a person, he establishes quantum mechanics with Feynman, Heisenberg, Schrodinger, etc. in the midst of the geniuses of the early 20th century. In particular, he won the Nobel Prize at the same time as Schrodinger. In considering Dirac’s personality, I would like to mention his family for a moment.

His family transferred nationality from Switzerland when Dirac was in his late teens. And it seems that the family environment was a big factor in talking about Dirac’s personality formation. First, in 1924, Dirac’s brother died himself. Was he the end of many thoughts? It seems that Dirac himself had many difficult conversations with his father. And he seems to have become an extremely reticent person.

Dirac and math

However, Dirac has achieved brilliant results by making full use of mathematics without sinking into the darkness. Especially the delta function and bracket notation are great. I left a lot of such footprints.

The delta function is a family of generalized functions defined using integrals. It is a useful function in many fields, but in the field of physics, it is possible to express how the wave packet converges with observation. Heaviside functions can be expressed mathematically. Various observations can be made depending on how the phenomenon is perceived, and the mathematical expression differs between when thinking about things from the perspective of the frequency axis and when thinking from the perspective of the actual coordinate axis (from the perspective of length). Analysis that applies this viewpoint engineeringly is also very convenient in practical use, and business analysis can be easily performed with a commercially available analyzer.

Bra-ket notation is a notation that uses the “parentheses” symbol in Japanese. In that formulation
Only the “<” part in the shape of the key bracket <> is called the “bra vector”.
Only the “>” part in the shape of the key bracket <> is called the “ket vector”.
The bra part is a vector amount in a very easy-to-understand expression
The part of the ket corresponding to is the formulation corresponding to the amount of vector acting on it.

Eigenstate and dirac

It is expressed as having an eigenstate when the pre-acting ket has an eigenvalue. It was impressive to me when I was an undergraduate that the vector here is a Hilbert vector (corresponding to infinite dimensions). I felt that the state corresponding to the physical quantity was described in an instant. From high school, when I could only imagine that one dimension was a line, two dimensions were a plane, and three dimensions were a three-dimensional space, my imagination expanded greatly, and the story suddenly expanded to infinite dimensions. One vector carries a lot of information. On the other hand, I think that the delta function expresses how the observation causes the wave function collapse in an instant.

Dirac is proceeding with this formulation and has come up with substances proposed by theory. A number of specific antimatter entities have been proposed and found. Antimatter is not routine because it has a slightly shorter lifespan than normal matter, but it is an important factor when discussing the formation and annihilation of particles. Protons have antiprotons and neutrons have antineutrons.

Dirac visits Japan

And above all, Dirac is a reticent person. While he has produced many achievements, he seems to have come to Japan as he was invited to the Physical Society of Japan. He just doesn’t have much anecdotes because he has a personality. There is no such thing as “when I drank tea with Nishina-san …”. Of course, it seems that Mr. Tomonaga and Mr. Yukawa, who are younger, were even more difficult to talk to.

He would have been silent when he spoke. Perhaps there was little daily conversation in the Netherlands. In Cambridge, the unit “1 Dirac” was used. As for the meaning within the group, “1 Word / 1 Hours” is equivalent to “1 Dirac”, and if two words are used per hour, it is converted as “2 Dirac” consumed. Dirac left only a few words per hour.

However, it seems that such Dirac was taken care of by the people around him because of his serious personality and personality that does not deceive people. The group photo used on the TOP screen of this blog is also in the center of the middle row. I feel that Einstein and Mrs. Curie care about the young genius Dirac and respect him with the feeling that “Your research is wonderful. Please continue to do your best!”

And Dirac is also a man who inherited the British tradition.
He was a Lucas professor in Cambridge. This honor begins with the first Isaac Barrow, continues with the second Isaac Newton, and has recently been inherited by Dr. SW Hawking, who has made a name for himself in cosmology.