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There exists an extensive literature for discretization of the abelian and the non-abelian gauge theories, known as lattice QED and lattice QCD, respectively. Here we will only sketch the main idea. Let us for simplicity use Euclidean signature $(+,+,+,+)$. A small Wilson-loop $$\tag{1} W~=~{\rm Tr}{\cal P}e^{ig\int_{\gamma}A}$$ lies approximately in a ...

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