## Abstract

In many areas of theoretical physics we encounter fields defined on a spacetime *M* taking values in some other space *F*. For instance, presume *F* as a real finite-dimensional vector space, then *∅* : M → *F* is a vector field. More generally, we can consider a family of spaces {*F*_{x}}*x*ϵ*M* varying over the points on M, that is *∅*(*x*) ϵ *F*_{x} for each *x* ϵ *M*. A field *∅* is then understood as a *section* from the spacetime manifold into the bundle of spaces over *M*. This is exactly the idea encoded in the mathematical theory of *fiber bundles*. Namely, fiber bundles provide a tool to describe the global structure of physical fields.

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© Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2019