A large diffeomorphism does not approach the identity at the relevant boundary or cannot be continuously deformed to the identity within the allowed gauge transformations. It may therefore act nontrivially on physical states or boundary data.
A large spatial diffeomorphism changes spatial coordinates by a transformation that remains nonzero at large distance. In cosmology, suitable large spatial diffeomorphisms generate zero-momentum adiabatic modes.
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A **large diffeomorphism** refers to a diffeomorphism (a smooth, invertible map between differentiable manifolds with a smooth inverse) that can be smoothly deformed or transformed into another diffeomorphism in a way that allows for a significant change in the structure of the manifold. This concept is commonly encountered in the fields of differential geometry and topology.