Lattice gauge theory

A formulation of gauge field theories on a discrete spacetime lattice. It enables nonperturbative calculations, especially numerical simulations of quantum chromodynamics.

Wilson action: A lattice gauge theory action built from traces of products of link variables around elementary loops. Its plaquette terms approximate the continuum gauge-field action.
Lattice quantum chromodynamics: The lattice formulation and numerical study of quantum chromodynamics, the theory of quarks and gluons. It is the best-established application, used to calculate hadron properties from first principles.
Gauge theory: A field theory whose descriptions have local redundancies, with interactions mediated by gauge fields. Lattice gauge theory discretizes this broader class of theories.
Perturbation theory: A method that approximates solutions by expanding in a small parameter such as a coupling constant. Lattice methods can address strongly coupled regimes where perturbative expansions fail.
Fermion sign problem: The cancellation or complex-weight problem that prevents straightforward importance sampling in many fermionic systems. It obstructs direct Monte Carlo calculations at nonzero baryon density.
Link variable: A group-valued variable assigned to a lattice edge, representing parallel transport of a gauge field. Link variables carry the gauge field while transforming locally at lattice sites.
Hadron spectrum: The set of masses and quantum numbers of composite particles made from quarks and gluons. Lattice simulations predict masses that can be compared with measured hadrons.
Lattice (group theory): A regular discrete arrangement of sites and links used to approximate spacetime in numerical field theory. Its geometry supplies the sites, directions, and spacing of the regulator.
Hamiltonian lattice gauge theory: A lattice formulation that discretizes space while retaining continuous time and uses a Hamiltonian description. It contrasts with Euclidean spacetime lattices commonly used for Monte Carlo calculations.
Real-time quantum field theory: Quantum field theory describing time evolution in real time rather than imaginary time. Euclidean simulations do not directly provide many real-time observables.

Linked from 11 pages