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Analytic Continuation of Complex Gauge Fields[Note 1. This article was presented at the Conference on Nonlinear ...]
Author(s) -
Harris Adam
Publication year - 1998
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00095
Subject(s) - holomorphic function , mathematics , normal bundle , vector field , pure mathematics , curvature , euclidean space , vector bundle , extension (predicate logic) , differential form , mathematical analysis , mathematical physics , geometry , computer science , programming language
The main result of this note treats the problem of unique extension of holomorphic gauge fields across closed subsets of complex Euclidean space, and is based on a corresponding extension theorem for holomorphic vector bundles due to N. P. Buchdahl and the author. Alternatively, let F be a unitary gauge field corresponding to a complex differential form of type (1, 1) (e.g., an anti self‐dual Yang–Mills field on a punctured ball in C 2 ). As a corollary of the main theorem, it is seen that a unique extension of such F , which preserves the curvature type, is obtained if the contraction of F with a holomorphic vector field lies in the image of the ∂¯‐operator of the associated holomorphic vector bundle.