|
In mathematical physics, a special conformal transformation is a type of spherical wave transformation and an expression of conformal symmetry. Special conformal transformations arise from translation of spacetime and inversion. The inversion can be taken〔Arthur Conway (1911) "On the application of quaternions to some recent developments of electrical theory", ''Proceedings of the Royal Irish Academy'' 29:1–9, particularly page 9〕 to be multiplicative inversion of biquaternions ''B''. The complex algebra ''B'' can be extended to P(''B'') through the projective line over a ring. Homographies on P(B) include translations: : The homography group G(''B'') includes : which provides the action of a special conformal transformation. ==Vector presentation== A special conformal transformation can also be written : It is a composition of an inversion (''x''μ → ''x''μ/x2), a translation (''x''μ → ''x''μ − ''b''μ), and an inversion: : Its infinitesimal generator is : ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「special conformal transformation」の詳細全文を読む スポンサード リンク
|