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group_theory:notions:central_extension [2017/04/09 14:24]
jakobadmin [Central Extension]
group_theory:notions:central_extension [2017/12/06 09:33] (current)
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 ===== Important Examples ===== ===== Important Examples =====
  
-  * The classical Galilean group needs to be extended by the introduction of a central charge, called //mass//, and this yields the Bargmann group. ​+  * The classical Galilean group needs to be extended by the introduction of a central charge, called //mass//, and this yields the Bargmann group. (This is shown very nicely in QUANTIZATION ON A LIE GROUP: HIGHER-ORDER POLARIZATIONS by V. Aldaya, J. Guerrero and G. Marmo).
   * The standard spatial rotation group $SO(3)$ needs to be extended by $\mathbb{Z}_2$,​ which yields $SU(2)$, because otherwise we are not able to describe spin $\frac{1}{2}$ particles.   * The standard spatial rotation group $SO(3)$ needs to be extended by $\mathbb{Z}_2$,​ which yields $SU(2)$, because otherwise we are not able to describe spin $\frac{1}{2}$ particles.
   * The algebra of fermionic non-Abelian charge densitites needs to be extended to the Mickelsson-Faddeev algebra (See [[http://​physics.stackexchange.com/​a/​76653/​37286|this answer]])   * The algebra of fermionic non-Abelian charge densitites needs to be extended to the Mickelsson-Faddeev algebra (See [[http://​physics.stackexchange.com/​a/​76653/​37286|this answer]])
group_theory/notions/central_extension.txt ยท Last modified: 2017/12/06 09:33 (external edit)