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In lattice gauge theory, the spacetime is Wick rotated into Euclidean space and discretized into a lattice with sites separated by distance and connected by links. In the most commonly considered cases, such as lattice QCD, fermion fields are defined at lattice sites (which leads to fermion doubling), while the gauge fields are defined on the links.
In physics, Hamiltonian lattice gauge theory is a calculational approach to gauge theory and a special case of lattice gauge theory in which the space is discretized but time is not. The Hamiltonian is then re-expressed as a function of degrees of freedom defined on a d-dimensional lattice.
Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD ...
[3] [4] The toric code can also be considered to be a Z 2 lattice gauge theory in a particular limit. [5] It was introduced by Alexei Kitaev. The toric code gets its name from its periodic boundary conditions, giving it the shape of a torus. These conditions give the model translational invariance, which is useful for analytic study.
In condensed matter physics and quantum information theory, the quantum double model, proposed by Alexei Kitaev, is a lattice model that exhibits topological excitations. [1] This model can be regarded as a lattice gauge theory, and it has applications in many fields, like topological quantum computation , topological order , topological ...
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 "gauge covariant" version of a gauge theory accounts for this effect by introducing a gauge field (in mathematical language, an Ehresmann connection) and formulating all rates of change in terms of the covariant derivative with respect to this connection. The gauge field becomes an essential part of the description of a mathematical ...
In pure gauge theory they play the role of order operators for confinement, where they satisfy what is known as the area law. Originally formulated by Kenneth G. Wilson in 1974, they were used to construct links and plaquettes which are the fundamental parameters in lattice gauge theory. [1]