Search results
Results from the WOW.Com Content Network
Lattice path of length 5 in ℤ 2 with S = { (2,0), (1,1), (0,-1) }.. In combinatorics, a lattice path L in the d-dimensional integer lattice of length k with steps in the set S, is a sequence of vectors ,, …, such that each consecutive difference lies in S. [1]
The graphs determine the local equations of motion, while the allowed large-scale configurations describe non-perturbative physics. But because Feynman propagators are nonlocal in time, translating a field process to a coherent particle language is not completely intuitive, and has only been explicitly worked out in certain special cases.
An n-path from an n-tuple (,, …,) of vertices of G to an n-tuple (,, …,) of vertices of G will mean an n-tuple (,, …,) of paths in G, with each leading from to . This n -path will be called non-intersecting just in case the paths P i and P j have no two vertices in common (including endpoints) whenever i ≠ j {\displaystyle i\neq j} .
In mathematics, the Schröder number, also called a large Schröder number or big Schröder number, describes the number of lattice paths from the southwest corner (,) of an grid to the northeast corner (,), using only single steps north, (,); northeast, (,); or east, (,), that do not rise above the SW–NE diagonal.
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously about the self-avoiding ...
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
The reciprocal lattices (dots) and corresponding first Brillouin zones of (a) square lattice and (b) hexagonal lattice. In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space.
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 going in the direction denoted by (). Four links around a single square are known as a plaquette, with their trace forming the smallest Wilson loop. [ 16 ]