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group_theory:notions:central_extension

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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)