I've a questions about the difference between small and large gauge transformations (a small gauge transformation tends to the identity at spatial infinity, whereas the large transformations don't). Many sources state (without any explanation or reference) that configurations related by small gauge transformations are physically equivalent, whereas large gauge transformations relate physically distinct configurations. This seems odd to me (and some lecturers at my university even say that this is wrong), because all gauge transformations relate physically equivalent configurations.
Some of the literature that mentions the difference between small and large gauge transformations:
In Figueroa-O'Farrill's notes it is mentioned in section 3.1 (page 81-82) in http://www.maths.ed.ac.uk/~jmf/Teaching/EDC.html
In Harvey's notes, see equation (2.13) in http://arxiv.org/abs/hep-th/9603086
In Di Vecchia's notes, see the discussion above (and below) equation (5.7) http://arxiv.org/abs/hep-th/9803026
They all say that large gauge transformation relate physically distinct configurations, but they don't explain why this is true. Does anybody know why this is true?