Special conformal transformation
Special conformal transformations arise from translation of spacetime and inversion. The inversion can be taken 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.
A special conformal transformation can also be written
Its infinitesimal generator is
- 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
- Di Francesco; Mathieu, Sénéchal (1997). Conformal field theory. Graduate texts in contemporary physics. Springer. pp. 97–98. ISBN 978-0-387-94785-3.
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