The action of conformal transformations on gauge potentials can be defined in a gauge-covariant fashion. This unconventional procedure is used in several branches of theoretical physics, with the consequence that gauge potentials do not transform according to a representation of the conformal group; rather, they provide a representation for the "group of paths" of the conformal group. The nonintegrable phase factor is central to the construction.
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R. Jackiw (1978) studied this question.
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