advanced_tools:group_theory:su2
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advanced_tools:group_theory:su2 [2020/09/07 04:19] 14.161.7.200 [Concrete] |
advanced_tools:group_theory:su2 [2025/03/08 21:24] (current) edi [Concrete] |
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| + | The Lie group $SU(2)$ describes all possible 3D 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 $SU(2)$ in its upper branch and a 3-dimensional representations of the same group in the lower branch. An important application of these two representations is the rotation of the quantum state of a spin-1/2 and a spin-1 particle, respectively. For a more detailed explanation of this diagram and more representations of $SU(2)$ see [[https://esackinger.wordpress.com/rotation-in-3-dimensions-and-angular-momentum/#su2|Fun with Symmetry]]. |
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| + | [{{ :advanced_tools:group_theory:su2_qm_spin.jpg?nolink }}] | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
advanced_tools/group_theory/su2.1599445144.txt.gz · Last modified: 2020/09/07 04:19 by 14.161.7.200
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