Rotations in 3-dimensional Euclidean space ... form the poster child of group theory and are almost indispensable in physics. Think of rotating a rig… - Anthony Zee

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Rotations in 3-dimensional Euclidean space ... form the poster child of group theory and are almost indispensable in physics. Think of rotating a rigid object, such as a bust of Newton. After two rotations in succession, the bust, being rigid, has not been deformed in any way; it merely has a different orientation. Thus, the composition of two rotations is another rotation.

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About Anthony Zee

Anthony Zee (, b. 1945) (Zee comes from the Shanghainese pronunciation of 徐) is a Chinese-American physicist and author.

Also Known As

Alternative Names: Xu Yihong

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Ah, group theory! The entire subject is amazing and amusing. Who would have expected that three Platonic solids—the cube, tetrahedron, and icosahedron—would pop up in constructing the Dynkin diagrams of the exceptional Lie algebras? Or that finite group theory could determine the remainder when 10<sup>10</sup> is divided by 11?

... the fight for credit goes on in every field, but in theoretical physics, it is almost a way of life, since ideas are by nature ethereal. And the stakes are high: the victor gets to go to Stockholm, while the loser is consigned to the dustbin of history; a history largely written by the victor with the help of an army of idolaters and science writers.

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It is difficult to overstate the importance (not to speak of the beauty) of what we have learned: The exchange of a spin 0 particle produces an attractive force, of a spin 1 particle a repulsive force, and of a spin 2 particle an attractive force, realized in the hadronic strong interaction, the electromagnetic interaction, and the gravitational interaction, respectively. The universal attraction of gravity produces an instability that drives the formation of structure in the early universe. ... Denser regions become denser yet. The attractive nuclear force mediated by the spin 0 particle eventually ignites the stars. Furthermore, the attractive force between protons and neutrons mediated by the spin 0 particle is able to overcome the repulsive electric force between protons mediated by the spin 1 particle to form a variety of nuclei without which the world would certainly be rather boring. The repulsion between likes and hence attraction between opposites generated by the spin 1 particle allow electrically neutral atoms to form.
The world results from a subtle interplay among spin 0, 1, and 2.
In this lightning tour of the universe, we did not mention the weak interaction. In fact, the weak interaction plays a crucial role in keeping stars such as our sun burning at a steady rate.

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