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In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops.They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops.
We evaluate the action of this operator on the Wilson loop as a calculation in the connection representation and rearranging the result as a manipulation purely in terms of loops (one should remember that when considering the action on the Wilson loop one should choose the operator one wishes to transform with the opposite factor ordering to ...
This is the case of the Wilson loop, which is defined as a path-ordered exponential to guarantee that the Wilson loop encodes the holonomy of the gauge connection. The parameter σ that determines the ordering is a parameter describing the contour , and because the contour is closed, the Wilson loop must be defined as a trace in order to be ...
The action of this operator on the Wilson loop is evaluated as a calculation in the connection representation and the result is rearranged purely as a manipulation in terms of loops (with regard to the action on the Wilson loop, the chosen transformed operator is the one with the opposite factor ordering compared to the one used for its action ...
In lattice field theory, the Wilson action is a discrete formulation of the Yang–Mills action, forming the foundation of lattice gauge theory. Rather than using Lie algebra valued gauge fields as the fundamental parameters of the theory, group valued link fields are used instead, which correspond to the smallest Wilson lines on the lattice .
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The most often studied class of gauge invariant operators are Wilson loops. A Wilson loop is the holonomy around a loop in M, traced in a given representation R of G. As we will be interested in products of Wilson loops, without loss of generality we may restrict our attention to irreducible representations R.
Kreek recalled Wilson’s pleading for a similar treatment for alcoholism. “Bill would say, ‘Vince, please develop a methadone maintenance treatment for alcoholism. AA is very helpful, but as you know most relapse…And that’s the bottom line, ’ ” Kreek said.