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advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye

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advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2023/02/20 18:45]
edi [Intuitive]
advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2023/03/19 21:45] (current)
edi [Concrete]
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 <tabbox Intuitive> ​ <tabbox Intuitive> ​
  
-The trivial representation maps all group elements to the identity ​matrix. This representation exists for any group.+The trivial representation maps all group elements to the identity ​element. This representation exists for any group.
  
-Spin-$0$ particles ​and fields ​transform under the trivial representation of $SU(2)$. That is, their spin value does not change ​when being rotated.+Spin-$0$ particles transform under the trivial representation of $SU(2)$. That is, their spin value does not change ​under rotation.
  
-The action (and often the Lagrangian) transforms under the trivial representation of space-time ​and gauge symmetry ​groups. That is, the action is not affected by these symmetry transformations.+The action (and often the Lagrangian) transforms under the trivial representation of the Lorentz group and the relevant ​gauge  groups. That is, the action is not affected by these symmetry transformations.
  
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 [{{ :​advanced_tools:​group_theory:​representation_theory:​su2_1d_rep.jpg?​nolink }}] [{{ :​advanced_tools:​group_theory:​representation_theory:​su2_1d_rep.jpg?​nolink }}]
  
-For a more detailed explanation of this diagram see [[https://​esackinger.wordpress.com/​|Fun with Symmetry]]. ​+For a more detailed explanation of this diagram see [[https://​esackinger.wordpress.com/​blog/​lie-groups-and-their-representations/#​su2_1d_rep|Fun with Symmetry]]. ​
    
 <tabbox Abstract> ​ <tabbox Abstract> ​
advanced_tools/group_theory/representation_theory/dean_proffesor_reza_sanaye.1676915118.txt.gz ยท Last modified: 2023/02/20 18:45 by edi