advanced_tools:group_theory:lie_groups

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+ | ====== Lie Groups ====== | ||

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+ | <tabbox Why is it interesting?> | ||

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+ | Lie groups describe continuous symmetry and lie at the heart of modern physics. For example, the symmetry group of the [[models:standard_model|standard model of particle physics]] and the best spacetime symmetry group that we know (the Poincare group) are Lie groups. | ||

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+ | <tabbox Layman> | ||

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+ | A Lie group is a continuous set of transformations that satisfy the [[advanced_tools:group_theory:|group axioms]]. A good example for a Lie group is the symmetry group of the circle. A rotation by $5^\circ$ is a symmetry of the circle and a rotation by $0.00001^\circ$ is a symmetry, too. In contrast, the symmetry group of a square is not continuous. A rotation by $90^\circ$ is a symmetry, whereas a rotation by $5^\circ$ is not a symmetry. | ||

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+ | <tabbox Student> | ||

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+ | See the recommendations [[advanced_tools:group_theory|here]]. | ||

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+ | <tabbox Researcher> | ||

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+ | <note tip> | ||

+ | The motto in this section is: //the higher the level of abstraction, the better//. | ||

+ | </note> | ||

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+ | <tabbox Examples> | ||

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+ | --> Example1# | ||

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+ | <-- | ||

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+ | --> Example2:# | ||

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+ | <-- | ||

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+ | <tabbox FAQ> | ||

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+ | <tabbox History> | ||

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+ | </tabbox> | ||

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advanced_tools/group_theory/lie_groups.txt ยท Last modified: 2017/12/17 10:23 (external edit)

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