Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-02-18
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, Latex
Scientific paper
Quaternionic formulation of D=4 conformal group and of its associated twistors and their relation to harmonic analyticity is presented. Generalization of $SL(2,\cal{C})$ to the D=4 conformal group SO(5,1) and its covering group $SL(2,\cal{Q})$ that generalizes the euclidean Lorentz group in $R^4$ [namely $SO(3,1)\approx SL(2,\cal{C})$ which allow us to obtain the projective twistor space $CP^3$] is shown. Quasi-conformal fields are introduced in D=4 and Fueter mappings are shown to map self-dual sector onto itself (and similarly for the anti-self-dual part). Differentiation of Fueter series and various forms of differential operators are shown, establishing the equivalence of Fueter analyticity with twistor and harmonic analyticity. A brief discussion of possible octonion analyticity is provided.
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