Group theory is the theory of mathematics that deals with symmetries. Group theory allows us to exhaustively and systematically derive symmetrical patterns.
In a crystal, atoms are arranged regularly in three dimensions. If you know group theory, you can see that even if there are various patterns in the crystal structure, it will be one of the patterns derived from group theory.
In physics, the subject of research is what happens to atoms when the pattern is established.
In my master's thesis, when I simulated the crystal structure of ice, I made a mistake in the initial configuration and converged on a crystal structure I had never seen before. At this time, my supervisor researched what the structure was classified in group theory.
At the presentation of my master's thesis, I announced that I had discovered a new crystal structure. After the presentation, another professor said, "This time, we have found one of the optimal solutions in terms of energy. If we can see how stable the structure is from an entropy point of view, it will be a better research." Thank you for your advice.
Phenomena such as "the same pattern is repeated", "there is a cycle in the way of transition", and "there is symmetry in the pattern, and there are synchronic and synchronous changes" can be expressed by group theory. .
Structuralism interprets such phenomena as occurring within a single structure of human society.
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