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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.
[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.
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 ...
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.
Simon Marcus Catterall (born 1964) is an American physicist at Syracuse University. [1] His research involves High Energy Theory, particularly Lattice field theory. [2] [3]He was elected Fellow of the American Physical Society in 2016 for For numerous important contributions to computational physics and Lattice field theory through studies of gravity, technicolor, and especially the lattice ...
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.
In lattice field theory, Wilson lines and loops play a fundamental role in formulating gauge fields on the lattice. The smallest Wilson lines on the lattice, those between two adjacent lattice points, are known as links, with a single link starting from a lattice point n {\displaystyle n} going in the μ {\displaystyle \mu } direction denoted ...