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advanced_tools:group_theory:su2 [2020/09/07 04:19] 14.161.7.200 [Concrete] |
advanced_tools:group_theory:su2 [2020/12/05 18:29] edi [Intuitive] |
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<tabbox Intuitive> | <tabbox Intuitive> | ||
+ | The Lie group $SU(2)$ describes all possible rotations of a spinorial object, that is, an object that needs to be rotated 720 degrees before returning to its initial state. A good example for such an object is a cube that is attached to a wall by belts: see the animations here [[https://en.wikipedia.org/wiki/Spinor]]. In physics, an important spinorial object is the fermion (e.g., an electron). | ||
- | <note tip> | + | For small rotations $SU(2)$ is identical to $SO(3)$, that is, both groups have the same Lie algebra. |
- | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | + | |
- | </note> | + | |
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<tabbox Concrete> | <tabbox Concrete> | ||
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**Representations** | **Representations** | ||
- | [{{ :advanced_tools:group_theory:su2reps.png?nolink |Diagram by Eduard Sackinger}}] | + | The diagram below shows the defining 2-dimensional representation of $SU(2)$, which describes spin-$1/2$ particles, in its upper branch. A 3-dimensional representations of the same group, which describes spin-$1$ particles, is shown in the lower branch. For an explanation of this diagram and more representations of $SU(2)$ see [[https://esackinger.wordpress.com/|Fun with Symmetry]]. |
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+ | [{{ :advanced_tools:group_theory:su2_qm_spin.jpg?nolink }}] | ||
<tabbox Abstract> | <tabbox Abstract> |