Euclidean space-time diffeomorphisms and their Fueter subgroups

Journal Article · Sat Feb 01 00:00:00 EST 1992 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529803· OSTI ID:5508511

Guersey, F; Jiang, W ^[1]

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1. Center for Theoretical Physics, Yale University, New Haven, Connecticut 06511 (United States)

Holomorphic Fueter functions of the position quaternion form a subgroup of Euclidean space-time diffeomorphisms. An {ital O}(4) covariant treatment of such mappings is presented with the quaternionic argument {ital x} being replaced by either {ital {bar p}x} or {ital x{bar p}} involving self-dual and anti-self-dual structures and {ital 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 Moebius 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.

• DOE Contract Number: AC02-76ER03075
• OSTI ID: 5508511
• Journal Information: Journal of Mathematical Physics (New York); (United States), Vol. 33:2; ISSN 0022-2488
• Country of Publication: United States
• Language: English

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