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Symmetry Elements

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  2. Wu-Ki Tung, Group theory in physics
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We apply the label symmetric to anything which stays invariant under some transformations. Conservation laws of physics are related to the symmetry of physical laws under various transformations. For instance, we expect the laws of physics to be unchanging in time. This is an invariance under "translation" in time, and it leads to the conservation of energy. Physical laws also should not depend on where you are in the universe. Such invariance of physical laws under "translation" in space leads to conservation of momentum. Invariance of physical laws under suitable rotations leads to conservation of angular momentum.

A general theorem that explains how conservation laws of a physical system must arise from its symmetries is due to Emmy Noether.

Group Theory | Scribd

Modern particle physics would not exist without group theory; in fact, group theory predicted the existence of many elementary particles before they were found experimentally. The structure and behavior of molecules and crystals depends on their different symmetries. Thus, group theory is an essential tool in some areas of chemistry.

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