High Quality Content by WIKIPEDIA articles! Clifford analysis, using Clifford algebras named after William Kingdon Clifford, is the study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications.Much of Clifford analysis works if we replace the complex Clifford algebra by a real Clifford algebra, Cln. This is not the case though when we need to deal with the interaction between the Dirac operator and the Fourier transform.Many Dirac type operators have a covariance under conformal change in metric. This is true for the Dirac operator in euclidean space, and the Dirac operator on the sphere under Moebius transformations. Consequently this holds true for Dirac operators on conformally flat manifolds and conformal manifolds which are simultaneously spin manifolds.

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