2003/02/18 by Sultan Catto, Catto, Sultan
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Elasticity and Wave Propagation #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Matrix Theory and Algorithms #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0302139
45 pages, Latex
openalex publication_date 2003/02/18 · arxiv created 2003/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quaternionic formulation of D=4 conformal group and of its associated twistors and their relation to harmonic analyticity is presented. Generalization of SL(2,\calC) to the D=4 conformal group SO(5,1) and its covering group SL(2,\calQ) that generalizes the euclidean Lorentz group in R4 [namely SO(3,1)≈ SL(2,\calC) which allow us to obtain the projective twistor space CP3] 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.