Inductive Construction of the Loop Transform for Abelian Gauge Theories

Details Inductive Construction of the Loop Transform for Abelian Gauge Theories Inductive Construction of the Loop Transform for Abelian Gauge Theories

2001-05-28

arxiv.org/abs/math-ph/0105041v1

Lett.Math.Phys. 57 (2001) 69-81

Physics

Mathematical Physics

to appear in Letters in Mathematical Physics

Scientific paper

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.

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