Infinitesimal natural and gauge-natural lifts
A natural bundle functor is defined as a prolongation functor from the category of manifolds into the category of bundles, which preserves the inclusions [\textit{A. Nijenhuis}, Differential Geometry, in Honor of Kentaro Yano, 317-334 (1972; Zbl 0246.53018)]. A gauge-natural bundle functor is defined to be a prolongation functor from the category of \(G\)- principal bundles to the category of fibred manifolds, which preserves embeddings and inclusions [\textit{D. J. Eck}, Mem. Am. Math. Soc. 247 (1981; Zbl 0493.53052)]. This paper is aimed at expressing naturality and gauge-naturality at infinitesimal level, by using the concept of strong systems of vector fields [\textit{M. Modugno}, Differential geometric methods in mathematical physics, Proc. 14th Int. Conf., Salamanca/Spain 1985, Lect. Notes Math. 1251, 236-264 (1987; Zbl 0614.53072)]. The main idea is to replace the action of a Lie group with the action of a Lie algebra of vector fields. The exposition involves largely jet techniques.
scientific article; zbMATH DE number 205000
scientific article