Chabysheva Sophia S, Hiller John R
Department of Physics, University of Minnesota-Duluth, Duluth, Minnesota 55812, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Dec;90(6):063310. doi: 10.1103/PhysRevE.90.063310. Epub 2014 Dec 17.
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the coordinates is one. These polynomials form a basis for the expansion of bosonic light-front momentum-space wave functions, as functions of longitudinal momentum, where momentum conservation guarantees that the fractions are on the interval [0,1] and sum to one. This generalizes earlier work on three-boson wave functions to wave functions for arbitrarily many identical bosons. A simple application in two-dimensional ϕ(4) theory illustrates the use of these polynomials.
我们提供了一种用于构造正交归一化多元多项式的算法，这些多项式在单位超立方体上关于任意两个坐标的互换是对称的，并且被约束在坐标之和为一的超平面上。这些多项式构成了玻色子光前动量空间波函数展开的基础，作为纵向动量的函数，其中动量守恒保证了分数在区间[0,1]内且总和为一。这将早期关于三玻色子波函数的工作推广到了任意多个相同玻色子的波函数。二维ϕ(4)理论中的一个简单应用说明了这些多项式的用途。
