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Some topics in Clifford analysis. (English) Zbl 1180.83004
Summary: This is a self-contained short course on some ideas on Clifford analysis with a classical application to physics. In the beginning we present quickly Clifford algebras stressing on structural periodicity, and the two points of view vector vs paravector. We list different partial differential operators; each of them may be the starting point of a function theory. Special relativity is discussed in detail. Some partial answers are given for the question of what is a good set of functions for Clifford analysis; this may be related to the question of the multiplication for functions. The question about special functions is unfortunately only sketched here.
Most of all this is known, but there are some unpublished (as far as I know) topics, by example: details on Frenet frames (“instantaneous comoving inertial frames”), Dirac magnetic monopole in the Clifford context, Fueter polynomials of vectorial type.
Many thanks to the organizers of the Toulouse congress who asked me to write this short course about a piece of Clifford analysis.

MSC:
83A05 Special relativity
83E05 Geometrodynamics and the holographic principle
15A66 Clifford algebras, spinors
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