document: In our study we illustrate the properties of gauge invariant extensions of local functionals. We aim at clarifying, via specific examples, the relation between a functional which is local in a particular gauge (but not necessarily gauge invariant), and its gauge invariant extension (which is not necessarily local). We show that the non-localities found are not perturbatively local because they cannot be expressed in terms of an infinite derivative expansion. We believe that the implications of this observation have not been clearly emphasised in the literature, as attested by the absence of any debate about it in recent works. It is precisely these dangerous infrared modes that make it hard to define a gauge independent renormalisation for the gauge invariant extensions of local functionals. This observation supports the remark in [2] that the expectation value receives important contributions from both large and small distances. Our arguments on renormalisability are based on the notion of renormalisation in the modern sense [8] which relies on BRST cohomology theorems. The BRST terminology will therefore be frequently used here, even though it is not always necessary.
doc_bio_tags: O O O O O O O O B I I I I I O O O O O O O O O O O B I I I I I I I O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I I O O B I I I I I O O O O O O O O O B I O O O O O O O O O O O O B O O O O B I I O O O O O O O O B I I O B I O O O O O O O O O O O O O
extractive_keyphrases: brst cohomology theorems brst terminology expectation value functional which is local in a particular gauge gauge independent renormalisation gauge invariant extensions of local functionals infrared modes its gauge invariant extension notion of renormalisation renormalisability
abstractive_keyphrases: invariant extensions of local functionals nfinite derivative expansion non-localities found