Abstract
Holomorphic Fueter functions of the position quaternion form a subgroup of Euclidean space-time diffeomorphisms. An O(4) covariant treatment of such mappings is presented with the quaternionic argument x being replaced by either p̄x or xp̄ involving self-dual and anti-self-dual structures and p denoting an arbitrary Euclidean time direction. An infinite group (the quasiconformal group) is exhibited that admits the conformal group SO(5,1) as a subgroup, in analogy to the two-dimensional case in which the Möbius group SO(3,1) is a subgroup of the infinite Virasoro group. The ensuing (3+1) covariant decomposition of diffeomorphisms suggests covariant gauges that throw the metric and the stress tensors in standard forms suitable for canonical quantization, leading to ‘‘improved’’ energy-momentum tensors. Other possible applications to current algebra and gravity will be mentioned.
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