Definition
An affine bundle of rank \(n\) is a bundle \(B\to X\) which is locally isomorphic to \(X\times \mathbb A^n\) and whose transition functions are affine functions.
Equivalently, \(\varphi:B\to X\) is said to be an affine bundle if it is a \(F\)-torsor for some rank \(n\) vector bundle \(F\to X\).