This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | Next revision Both sides next revision | ||
advanced_tools:group_theory:casimir_operators [2017/12/17 11:53] |
advanced_tools:group_theory:casimir_operators [2017/12/17 12:05] jakobadmin created |
||
---|---|---|---|
Line 1: | Line 1: | ||
+ | ====== Casimir Operators ====== | ||
+ | |||
+ | <tabbox Why is it interesting?> | ||
+ | |||
+ | Casimir operators are crucial to understand representations of groups and are often used as labels for [[advanced_notions:elementary_particles|elementary particles]]. | ||
+ | |||
+ | |||
+ | |||
+ | <tabbox Layman> | ||
+ | |||
+ | <note tip> | ||
+ | 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 Student> | ||
+ | |||
+ | The Casimir operators are those operators that can be built from the generators of a given group that commute with all generators of the group. Therefore their value is invariant and can be used to characterize the irreducible representations. | ||
+ | |||
+ | This means in practice that the Casimir operators simply yield a fixed (=invariant) number for each representation that we use to label representations. | ||
+ | |||
+ | <tabbox Researcher> | ||
+ | |||
+ | <note tip> | ||
+ | The motto in this section is: //the higher the level of abstraction, the better//. | ||
+ | </note> | ||
+ | |||
+ | | ||
+ | <tabbox Examples> | ||
+ | |||
+ | --> Example1# | ||
+ | |||
+ | |||
+ | <-- | ||
+ | |||
+ | --> Example2:# | ||
+ | |||
+ | |||
+ | <-- | ||
+ | |||
+ | <tabbox FAQ> | ||
+ | | ||
+ | <tabbox History> | ||
+ | |||
+ | </tabbox> | ||
+ | |||