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--- advanced_tools:group_theory:su2 [2020/09/07 04:19]
14.161.7.200 [Concrete]
+++ advanced_tools:group_theory:su2 [2023/04/17 03:23] (current)
edi [Concrete]
@@ Line 3: / Line 3: @@
 <tabbox Intuitive>
+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>
 <tabbox Concrete>
@@ Line 29: / Line 27: @@
 **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/blog/lie-groups-and-their-representations/#su2_qm_spin|Fun with Symmetry]].
+[{{ :advanced_tools:group_theory:su2_qm_spin.jpg?nolink }}]
 <tabbox Abstract>

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