ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The NLF–Lie group structure of the group G of the gauge transformations, defined as the group of sections of the bundle P[G] associated to the principal bundle P(M,G), is discussed. Other current definitions of the group of gauge transformations are shown to admit a nontrivial smooth structure only in the case of compact G. The space C of principal connections, as well, is given the structure of local affine NLF-manifold, after identifications of connections with sections of a convenient vector bundle on M. Finally, the smoothness of the action of G on C is proved in general. In the case of compact M, the group G becomes a tame Fréchet–Lie group and the action a tame smooth action.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527404
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