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A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material; Lattice (music), an organized grid model of pitch ratios; Lattice (pastry), an ornamental pattern of crossing strips of pastry
In physics, lattice field theory is the study of lattice models of quantum field theory.
Definition [ edit ] A lattice is a poset in which any two elements x {\displaystyle x} and y {\displaystyle y} have both a least upper bound, called the join or supremum , denoted by x ∨ y {\displaystyle x\vee y} , and a greatest lower bound, called the meet or infimum , denoted by x ∧ y {\displaystyle x\wedge y} .
Latticework may be functional – for example, to allow airflow to or through an area; structural, as a truss in a lattice girder; [2] used to add privacy, as through a lattice screen; purely decorative; or some combination of these. Latticework in stone or wood from the classical period is also called Roman lattice or transenna (plural transenne).
Filter theory was initially developed from earlier studies of transmission lines. [8] [9] In this theory, a filter section is specified in terms of its propagation constant and image impedance (or characteristic impedance). Specifically for the lattice, the propagation function, γ, and characteristic impedance, Z o, are defined by, [4]: 379 [6]
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 .