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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.
The basic idea is simply that the vacuum expectation values of Wilson loops in Chern–Simons theory are link invariants because of the diffeomorphism-invariance of the theory. To calculate these expectation values, however, Witten needed to use the relation between Chern–Simons theory and a conformal field theory known as the Wess–Zumino ...
In quantum field theory, the Polyakov loop is the thermal analogue of the Wilson loop, acting as an order parameter for confinement in pure gauge theories at nonzero temperatures. In particular, it is a Wilson loop that winds around the compactified Euclidean temporal direction of a thermal quantum field theory .
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.
The S-matrix in quantum field theory is an example of a time-ordered product. The S-matrix, transforming the state at t = −∞ to a state at t = +∞, can also be thought of as a kind of "holonomy", analogous to the Wilson loop. We obtain a time-ordered expression because of the following reason: We start with this simple formula for the ...
The 't Hooft loop is a disorder operator since it creates singularities in the gauge field, with their expectation value distinguishing the disordered phase of pure Yang–Mills theory from the ordered confining phase. Similarly to the Wilson loop, the expectation value of the 't Hooft loop can follow either the area law [5]
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory and the principle of relativity with ideas behind quantum mechanics. [ 1 ] : xi QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles .