Inductive Construction of the Loop Transform for Abelian Gauge Theories
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We construct the loop transform in the case of Abelian gauge theories as unitary operator given by the inductive limit of Fourier transforms on tori. We also show that its range, i.e.the space of kinematical states of the quantum loop representation, is the Hilbert space of square integrable complex valued functions on the group of loops.
to appear in Letters in Mathematical Physics
to appear in Letters in Mathematical Physics