This is realized most easily when the theory is based on flat spacetime R 1 , 3 , as then the base spacetime is contractible, and hence any fibre bundle is trivial. In gauge theory one considers principal bundles with the spacetime as its base manifold, where the fibre is a torsor of the gauge group G . Crucially, since the principal bundle must be trivial, there exists a global trivialization. In physics, one generally works under an implicit global trivialization and rarely in the more abstract principal bundle.