Abstract
Let G be a Lie group, with Lie algebra g, and let U be an open subset of R n. A gauge field on U is a field A μ , of vectors with lower indices (covectors), taking values in the Lie algebra g. A field with values in a vector space of dimension r can be thought of as an r-tuple of real-valued fields (fields in the familiar sense): thus, if we choose a basis (e l,...,e r ) for g, we can express A μ (x) in the form \({A_u}\left( \chi \right) = A_u^k\left( \chi \right)ek\) where the \(A_u^k\left( \chi \right) \) (for k fixed) specify a real-valued vector field on U.
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© 1994 Springer-Verlag Berlin Heidelberg
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Schwarz, A.S. (1994). Geometry of Gauge Fields. In: Topology for Physicists. Grundlehren der mathematischen Wissenschaften, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02998-5_16
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DOI: https://doi.org/10.1007/978-3-662-02998-5_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08131-6
Online ISBN: 978-3-662-02998-5
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