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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 .
The ability to vary the gauge potential at different points in space and time (by changing (,)) without changing the physics is called a local invariance. Electromagnetic theory possess the simplest kind of local gauge symmetry called () (see unitary group). A theory that displays local gauge invariance is called a gauge theory.
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.
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 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 ...
Creutz's research spans a wide variety of topics in particle physics and mathematical physics, but he is best known for his work on lattice QCD. [4] His 1983 textbook Quarks, Gluons, and Lattices was the first full-length textbook on lattice QCD and is considered a classic in the field.
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.
Her research considers lattice gauge theories and how they couple to fermionic matter. [7] She performs quantum simulations of many-body physics. These simulations can achieve with a high degree of control and can achieve complex physical behaviour, including many-body localization and Hilbert space fragmentation. [8]