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advanced_tools:group_theory:su2

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advanced_tools:group_theory:su2 [2020/12/05 18:29]
edi [Intuitive]
advanced_tools:group_theory:su2 [2020/12/26 22:52]
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).+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).
  
 For small rotations $SU(2)$ is identical to $SO(3)$, that is, both groups have the same Lie algebra. For small rotations $SU(2)$ is identical to $SO(3)$, that is, both groups have the same Lie algebra.
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 **Representations** **Representations**
  
-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]].+The diagram below shows the defining ​(2-dimensionalrepresentation 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/​|Fun with Symmetry]].
  
 [{{ :​advanced_tools:​group_theory:​su2_qm_spin.jpg?​nolink }}] [{{ :​advanced_tools:​group_theory:​su2_qm_spin.jpg?​nolink }}]
advanced_tools/group_theory/su2.txt ยท Last modified: 2020/12/26 22:52 by edi