Clifford Algebra of Spacetime and the Conformal Group
نویسندگان
چکیده
We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. A Clifford space (that contains spacetime, in particular) does not contain only points (events), but also lines, surfaces, volumes, etc.. All those geometric objects are very elegantly and compactly described by means of the geometric calculus based on Clifford algebra. A subgroup of the Clifford algebra of spacetime is the conformal group SO(4,2) which can naturally be given the active interpretation. To finalize we show why relativity in Clifford spaces implies scale changes of physical objects as a result of free motion, without the presence of forces, advocated long ago by one of us. This represents a true dilatational motion of physical objects in Clifford spaces.
منابع مشابه
ep - t h / 02 03 19 4 v 2 1 0 N ov 2 00 3 Clifford Algebra of Spacetime and the Conformal Group
We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. The latter algebra is a manifold, called Clifford space, which is assumed to be the arena in which physics takes place. A Clifford space does not contain only points (events), but also lines, surfaces, volumes, etc..., and thus provides a framework for description of extended objects. A subspace ...
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