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advanced_tools:group_theory:central_extension

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advanced_tools:group_theory:central_extension [2017/12/17 11:12]
jakobadmin
advanced_tools:group_theory:central_extension [2017/12/17 10:26] (current)
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 For example, the projective representations of  $SO(3,1)$ correspond to regular representations of $SL(2,​\mathbb{C})$. ​ For example, the projective representations of  $SO(3,1)$ correspond to regular representations of $SL(2,​\mathbb{C})$. ​
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 +<​blockquote>"​Central extensions play an important role in quantum mechanics: one of the earlier encounters is by means of Wigner’s theorem which states that a symmetry of a quantum mechanical system determines a (anti-) unitary transformation of the Hilbert space, which is unique up to a phase factor $e^{iϑ}$. As an immediate consequence of this phase factor, one deduces that given a quantum mechanical symmetry group $G$ there exists an extension $G_0$ of $G$ by $U(1)$ (the phase factors) which acts as a group of unitary transformations on the Hilbert space. **In most cases physicists have been succesful in hiding these central extensions by using larger symmetry groups**"​ <​cite>​http://​math.univ-lille1.fr/​~gmt/​PaperFolder/​CentralExtensions.pdf</​cite></​blockquote>​
  
 <tabbox Layman> ​ <tabbox Layman> ​
advanced_tools/group_theory/central_extension.txt · Last modified: 2017/12/17 10:26 (external edit)