Six-dimensional space: Difference between revisions

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In mathematics, a '''special conformal transformation''' is a member of the [[Conformal symmetry|conformal symmetry group]]. It is given by<ref>{{cite book |last = Di Francesco |coauthors= Mathieu, Sénéchal |title= Conformal field theory |series= Graduate texts in contemporary physics |year= 1997 |publisher= Springer |isbn= 978-0-387-94785-3 |pages= 97–98}}</ref>
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:<math> x'^\mu = \frac{x^\mu-b^\mu x^2}{1-2b\cdot x+b^2x^2} \,. </math>
Its [[Generating set of a group|infinitesimal generator]] is
:<math> K_\mu = -i(2x_\mu x^\nu\partial_\nu - x^2\partial_\mu) \,. </math>


Such a transformation can also be written as sequence of an [[Inversive geometry|inversion]] (''x''<sup>μ</sup>&nbsp;→&nbsp;''x''<sup>μ</sup>/x<sup>2</sup>), a [[translation (physics)|translation]] (''x''<sup>μ</sup>&nbsp;→&nbsp;''x''<sup>μ</sup>&nbsp;−&nbsp;''b''<sup>μ</sup>), and an inversion:
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:<math> \frac{x'^\mu}{x'^2} = \frac{x^\mu}{x^2} - b^\mu \,. </math>
 
==References==
<references/>
 
{{geometry-stub}}
 
[[Category:Symmetry]]
[[Category:Scaling symmetries]]
[[Category:Conformal field theory]]

Revision as of 02:08, 22 February 2014

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