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Wilson loop. 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.
Originally, solvable two-dimensional lattice gauge theories had already been introduced in 1971 as models with interesting statistical properties by the theorist Franz Wegner, who worked in the field of phase transitions. When only 1×1 Wilson loops appear in the action, lattice gauge theory can be shown to be exactly dual to spin foam models.
The gauge invariance and the metric invariance can be viewed as the invariance under the adjoint Lie group action in the Chern–Weil theory. The action integral (path integral) of the field theory in physics is viewed as the Lagrangian integral of the Chern–Simons form and Wilson loop, holonomy of vector bundle on M.
Wilson 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 ...
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations according to certain smooth families of operations ( Lie groups ). Formally, the Lagrangian is invariant . The term gauge refers to any specific mathematical formalism to regulate ...
Polyakov loop. 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.
v. t. e. Attempts have been made to describe gauge theories in terms of extended objects such as Wilson loops and holonomies. The loop representation is a quantum hamiltonian representation of gauge theories in terms of loops. The aim of the loop representation in the context of Yang–Mills theories is to avoid the redundancy introduced by ...
In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). [1] [2] A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand ...