Chabysheva Sophia S, Elliott Blair, Hiller John R
Department of Physics, University of Minnesota-Duluth, Duluth, Minnesota 55812, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):063307. doi: 10.1103/PhysRevE.88.063307. Epub 2013 Dec 16.
We develop a polynomial basis to be used in numerical calculations of light-front Fock-space wave functions. Such wave functions typically depend on longitudinal momentum fractions that sum to unity. For three particles, this constraint limits the two remaining independent momentum fractions to a triangle, for which the three momentum fractions act as barycentric coordinates. For three identical bosons, the wave function must be symmetric with respect to all three momentum fractions. Therefore, as a basis, we construct polynomials in two variables on a triangle that are symmetric with respect to the interchange of any two barycentric coordinates. We find that, through the fifth order, the polynomial is unique at each order, and, in general, these polynomials can be constructed from products of powers of the second- and third-order polynomials. The use of such a basis is illustrated in a calculation of a light-front wave function in two-dimensional ϕ(4) theory; the polynomial basis performs much better than the plane-wave basis used in discrete light-cone quantization.
我们开发了一种多项式基，用于光前福克空间波函数的数值计算。此类波函数通常取决于总和为1的纵向动量分数。对于三个粒子，此约束将剩余的两个独立动量分数限制在一个三角形内，其中三个动量分数用作重心坐标。对于三个相同的玻色子，波函数必须相对于所有三个动量分数对称。因此，作为一个基，我们在一个三角形上构造两个变量的多项式，这些多项式在任意两个重心坐标互换时是对称的。我们发现，到五阶为止，多项式在每个阶都是唯一的，并且一般来说，这些多项式可以由二阶和三阶多项式的幂的乘积构成。在二维ϕ(4)理论中光前波函数的计算中说明了这种基的使用；多项式基的表现比离散光锥量子化中使用的平面波基要好得多。
