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In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics , and include the prevailing theories of elementary particles : quantum electrodynamics , quantum chromodynamics (QCD) and particle physics' Standard Model .
Since then, he has been a program manager at the United States Department of Energy, Office of Science (SC), Office of High Energy Physics. Kogut is known for the Kogut–Susskind fermion and his collaboration with Leonard Susskind on the Hamiltonian formulation of Kenneth G. Wilson's lattice gauge theory. [1]
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.
The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge ...
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.
J. Smit, Introduction to Quantum Fields on a Lattice, Cambridge University Press 2002. H. Rothe, Lattice Gauge Theories, An Introduction, World Scientific 2005. T. DeGrand and C. DeTar, Lattice Methods for Quantum Chromodynamics, World Scientific 2006. C. Gattringer and C. B. Lang, Quantum Chromodynamics on the Lattice, Springer 2010.
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 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]